Ninth National Operator Theory and Operator Algebraic Conference
Report 1
Reporter: BAI Chaofang(Xiamen University)
Title: Coherence measure
Time: October 29,2017 (Sunday) PM 3:00-3:25
Location: Xiangzhou Hotel 7th Floor, Room B
Abstract: Quantum coherence provides an important resource for quantum information processing. There arises naturally the question of how it can be quantified, i.e., measuring coherence. In this talk, we will review several coherence measures and give a new one.
Report 2
Reporter: CAO Guangfu(South China Agricultural University)
Title: Spectral Theory of Multiplication Operators on Hardy-Sobolev Spaces
Time: October 29,2017 (Sunday) AM 9:20-10:00
Location: Xiangzhou Hotel 7th Floor, Room A
Abstract: For a pointwise multiplier $\varphi$ of the Hardy-Sobolev space $H^2_\beta$ on the open unit ball $bn$ in $cn$, we study spectral properties of the multiplication operator $M_\varphi: H^2_\beta\to H^2_\beta$. In particular, we compute the spectrum and essential spectrum of $M_\varphi$ and develop the Fredholm theory for these operators.
Report 3
Reporter: CHEN Xiaoman(Fudan University)
Title: Coarse geometry at infinity
Time: October 28,2017 (Saturday) PM 3:35-4:00
Report 4
Reporter: CHEN Yanni(Shaanxi Normal University)
Title: Commutative and Noncommutative Hardy spaces based on unitarily invariant norms
Abstract: The theory of Hardy spaces originated with discoveries made sixty years ago by famous mathematicians: Hardy, Littlewood, Riesz, Smirnov, which plays a central role in many parts of applied mathematics, e.g., systems theory, control theory, signal and image processing. As a more general $\|\|_p-$norm on the Hardy space, the unitarily invariant norms are very important in the study of function spaces, group representations and in obtaining certain bounds of importance in quantum field theory. Now it is natural to ask: \begin{enumerate}\item What does one get if one combines the classical Hardy spaces and unitarily invariant norms?
\item What does one get if one combines the theory of Arveson's noncommutative Hardy's spaces and unitarily invariant norms?\end{enumerate}
In this talk, replacing the $\|\|_p-$norms with unitarily invariant norms, we are going to introduce the generalized Hardy spaces and extend many classical results in the commutative and noncommutative Hardy spaces.
Report 5
Reporter: CHEN Zeqian (Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences)
Title: The geometric phase of quantum systems
Time: October 29,2017 (Sunday) AM 10:50-11:30
Abstract: In this talk, we will report that the geometric phase is introduced associated with quantal observable space. The phase is determined by the Heisenberg equation, contrary to the usual one by the Schrödinger equation. Geometrical interpretation of the phase over the quantal observable space is also presented.
Report 6
Reporter: CHENG Guozheng (Wenzhou University)
Title: Random Weighted Shift
Time: October 29,2017 (Sunday) PM 2:30-3:00
Abstract: In this taking, we firstly shall briefly review the past of Two projections theory. The subject is not only an old topic, but also a new topic in operator theory and operator algebra. More recently, the two projections theory has attracting attentions of a variety of mathematicians (see: A gentle guide to the basics of two projections theory, Linear Algebra Appl. 432 (2010) 1412-1459 ). After that we will present our recent researching results involving the two projections.
Report 7
Reporter: Du Hongke (Shaanxi Normal University)
Title: Two projections theory and applications
Time: October 29,2017 (Sunday) AM 8:40-9:20
Report 8
Reporter: DUAN Zhoubo (Taiyuan University of Technology)
Title: Contractive freedom for infinite-dimensional
Time: October 28,2017 (Saturday) PM 3:10-3:35
Abstract: The unitary freedom in ensemble of pure states with a given state and the
unitary in freedom operator-sumrepresentation for a given channel are no longer valid for infinite dimensional systems. Instead, what we can establish are the contractive freedom in ensemble and the contractive freedom in operator-sum representation. Namely, we show that,
(1) two ensembles and determine the same state if and only if there exists some contractive matrix such that for each i;
(2) two sequences Aj and Bj of Kraus operators in operator-sum representations determine the same channel if and only if there exists some contractive matrix such that for each i.
Report 9
Reporter: FANG Junsheng (Hebei Normal University)
Title: On a class of operators in the hyperfinite type II1 factor
Time: October 28,2017 (Saturday) PM 2:30-3:10
Abstract: In this talk, we introduce a class of operators in the hyperfinite type II1 factor. We will discuss the spectrum, Brown spectrum, invariant subspaces of the operators. We also characterize the von Neumann algebras and C*-algebras generated by the class of operators.
Report 10
Reporter: GUO Kunyu (Fudan University)
Title: Dirichlet series and Hilbert modules in infinitely many variables
Time: October 29,2017 (Sunday) AM 8:00-8:40
Abstract: The Hardy module $H^2(\mathbb{D}_2^{\infty})$ in infinitely many variables is closely related to some classical problems, such as the completeness problem and the Riesz basis problem of $L^2(0,1)$ concerning systems of dilated functions; and the problem of zero points of Dirichlet series. This inspires us to focuses on polynomial generated submodules of the Hardy module $H^2(\mathbb{D}_2^{\infty})$ in infinitely many variables. Since the polynomial ring $\mathcal{P}_{\infty}$ in infinitely many variables is not Noetherian, some standard tricks for finitely many variables fail to work. Therefore, we need to introduce new techniques to the situation of infinitely many variables. It is shown that some classical results of $H^2(\mathbb{D}^n)$ remain valid for infinitely many variables. However, some new phenomena indicate that the Hardy module $H^2(\mathbb{D}_2^{\infty})$ diverges considerably from the case in finitely many variables. This is a joint work with Hui Dan and Hansong Huang.
Report 11
Reporter: Hou Jinchuan (Taiyuan University of Technology)
Title: Characterizing the Gaussian coherence breaking channel and its property with assistant entanglement inputs
Time: October 28,2017 (Saturday) AM 9:00-9:40
Abstract: We give a characterization of arbitrary n-mode Gaussian coherence breaking channels (GCBCs) and show that the tensor product of a GCBC with an arbitrary Gaussian channel maps all input states into product states. The inclusion relations between the sets of GCBCs, Gaussian positive partial transpose channels (GPPTCs), entanglement breaking channels (GEBCs), Gaussian classical-quantumchannels (GCQCs) and Gaussian quantum-classical channels (GQCCs) are displayed.
Report 12
Reporter: HUANG Hansong (East China University of Science and Technology)
Title: Cyclic vectors in Fock-type spaces
Time: October 28,2017 (Saturday) PM 4:00-4:25
Abstract: In this talk, we study cyclic vectors in Fock-type spaces and completely characterize them.
Report 13
Reporter: HUANG Huichi (Chongqing University)
Title: The discrete quantum group fixing a sequence of finite sets
Time: October 29,2017 (Sunday) PM 4:00-4:25
Abstract: Motivated by a generalization of Szemeredi's theorem, we consider the discrete quantum subgroup fixing a sequence of finite subsets. Then we prove a generalized mean ergodic theorem for discrete quantum groups.
Report 14
Reporter: Liu Liu (Dalian University of Technology)
Title: The stability analysis of causal systems on the Hilbert resolution space
Abstract: The stability theory of causal linear systems on Hilbert resolution space is an important application of operator theory and non-self adjoint operator algebra theory to the control theory. Within the context of operator theory and operator algebra, some results on the factorization, stable rank, gap metric and time-varying (TV) gap of causal linear systems are introduced in this talk. It is shown that the TV gap has no advantage over gap metric in stability and robustness analysis on the Hilbert resolution space $(\ell^2(\mathbb{Z}_+):\{P_n\}_{n\in\mathbb{Z}_+})$, while it stands out on $(\ell^2(\mathbb{Z}):\{P_n\}_{n\in\mathbb{Z}})$.
Report 15
Reporter: JI Guoxing (Shaanxi Normal University)
Title: Pencils of Pairs of Projections
Time: October 29,2017 (Sunday) AM 11:30-12:00
Abstract: Let T be a self-adjoint operator on a complex Hilbert space H. We give a sufficient and necessary condition for T to be the pencil of a pair of projections at some point . Then we represent all pairs of projections such that for a fixed and find that all such pairs are connected if . Afterwards, the von Neumann algebra generated by such pairs is characterized. Moreover, we prove that there are at most two real numbers such that T is the pencils at these real numbers for some pairs of projections. Finally, we determine when the real number is unique.
Report 16
Reporter: JIANG Yongle(Skku University, Korea)
Title: On calculating the second cohomology group of Bernoulli shifts
Time: October 29,2017 (Sunday) PM 4:25-4:50
Abstract: In the early 2000, Popa initiated his powerful deformation/rigidity techniques in von Neumann algebras. In the past decades, many old questions in von Neumann algebras and related areas have been settled using these techniques. One of the early success is calculating the first cohomology group with the unit circle $\mathbb{T}$ as the target group for Bernoulli actions $G\curvearrowright (X_0, \mu)^G$ of property (T) groups (e.g. $G=SL_3(\mathbb{Z})$), i.e. it is shown that $H^1(G\curvearrowright X_0^G; \mathbb{T})=H^1(G, \mathbb{T})$. Motivated by this result, Popa asked whether the same result holds for the second cohomology group. We discuss the negative answer we get by using the idea of algebraic actions.
Report 17
Reporter: LI Hui(East China Normal University)
Title: Boundary Quotient C*-algebras of Products of Two Odometers
Abstract: The semigroups of products of 2 odometers, constructed by Brownlowe-Ram agge-Robertson-Whittaker, are generalizations of odometers. However, the boundary quotient C*-algebra of a product of 2 odometers was not well understood. In this talk I will firstly write down the explicit relations of the generators for the boundary quotient C*-algebra of a product of 2 odometers. Then for any product of 2 odometers I will construct a regular topological 2-graph associated to it, such that the boundary quotient C*-algebra of the product of 2 odometers is isomorphic to the topological 2-graph C*-algebra. This identification allows us to provide conditions under which the boundary quotient C*-algebra of the product of 2 odometers is amenable, simple, and purely infinite. This is joint work with Dilian Yang.
Report 18
Reporter: LI Qihui (East China University of Science and Technology)
Title: Wave operators and Kato-Rosenblum Theorem insemifinite von Neumann algebras
Time: October 28,2017 (Saturday) PM 5:30-5:55
Abstract: The wave operator is the basic object of scattering theory. In this talk, we will extend this concept to the setting of semifinite von Neumann algebras. By showing the existence of wave operators, we will provide a version of the Kato-Rosenblum theorem in a semifinite von Neumann algebras.
Report 19
Reporter: MA Zhenhua (Hebei Institute of Architectural Engineering)
Title: Some Topological Properties and Geometric Properties of Noncommutative Orlicz Spaces
Time: October 28,2017 (Saturday) PM 5:25-5:50
Report 20
Reporter: MA Pan (Central South University)
Title: Semicommutator and commutator of truncated Toeplitz operators
Time: October 29,2017 (Sunday) PM 3:25-3:50
Abstract: A necessary and sufficient condition is found on the semi-commutator of truncated Toeplitz operators with bounded symbol in model spaces which the corresponding inner function . Also, a uniform way to characterize the semicommutator and commutator of truncated Toeplitz operators is presented by the techniques of Toeplitz operators and Hankel operators on Hardy space.
Report 21
Reporter: MENG Qing (Qufu Normal University)
Title: Weak Haagerup property of W*-crossed products
Time: October 29,2017 (Sunday) PM 4:50-5:15
Abstract: We show that if $M\bar{\rtimes}_\alpha \Gamma$ has the weak Haagerup property, then both $M$ and $\Gamma$ have the weak Haagerup property. Let $\Gamma$ be an amenable group, then the weak Haagerup property of $M$ implies that of $M\bar{\rtimes}_\alpha \Gamma$. Moreover, we give a condition under which the weak Haagerup property of $M$ and $\Gamma$ imply that of $M\bar{\rtimes}_\alpha \Gamma$.
Report 22
Reporter: PENG Shuangjie (Huazhong Normal University)
Title: Local uniqueness reduced by concentration
Time: October 28,2017 (Saturday) AM 11:10-11:50
Abstract: We will talk about a type of elliptic equations with critical exponents and scalar curvature K(y), K(y) is positive and periodic in its first k variables (y_1,..., y_k). Under some conditions on K(y) near its critical point, we prove not only that this problem admits solutions with infinitely many bubbles, but also that the bubbling solutions obtained in our existence result are locally unique. This local uniqueness result implies that some bubbling solutions preserve the symmetry of K(y).
Report 23
Reporter: QI Xiaofei (Shanxi University)
Title: Strong 3-skew commutativity preserving maps on operator algebras
Time: October 28,2017 (Saturday) PM 4:35-5:05
Abstract: Let R be a unital prime *-ring containing a nontrivial symmetric idempotent. Let be a surjective map. It is shown that satisfies for all if and only if there exists with such that for all . Where I is the unit of R and Zs(R) is the symmetric center of R. This result then is applied to matrix algebras and operator algebras such as prime C*-algebras, factor von Neumann algebras, the indefinite self-adjoint standard operator algebras and symmetric standard operator algebras.
Report 24
Reporter: QIAO Yu (Shanxi Normal University)
Title: Fredholm Groupoids and Exhaustive Families of Representations of Groupoid Algebras
Time: October 28,2017 (Saturday) PM 5:05-5:30
Abstract: In this talk, we first review the primitive ideal space of a C*-algebra, exhaustive families of representations of C*-algebras (defined by Nistor and Prudhon), and groupoid C*-algebras (via representation theory of C*-algebras). Then we introduce the notions of Fredholm groupoids and Exel's strong property for groupoids.
We show that under suitable assumptions, a groupod with Exel's strong property is Fredholm. Finally we obtain the following theorem: if $\mathcal{G}$ is a locally compact, second countable, and Hausdorff groupoid with the unit space M, such that all isotropy groups $\mathcal{G}^x_x, x\in M$, are amenable，then $\mathcal{G}$ is metrically amenable and has Exel's strong property. Hence, combining these two results, we obtain a sufficient condition for a groupoid to be Fredholm. This is joint work with Catarina Carvalho and Victor Nistor.
Report 25
Reporter: SHI Luoyi (Tianjin Polytechnic University)
Title: Amenability, similarity and approximation
Abstract: The concept of amenability is fundamental in the study of operator algebras. Farenick, Forrest, Marcoux and Popov investigated the amenability of Banach algebras singly generated by Hilbert space operators. It is proved that the Banach algebra generated by T is amenable if and only if T is similar to a normal operator whose spectrum has a connected complement and an empty interior. The amenability of C*-algebras is closely related to another important notion called nuclearity, by the work of Connes and Haagerup, a C*-algebra is amenable if and only if it is nuclear. Inspired by the above mentioned works, we are interested in determining when a singly generated C*a-algebra is amenable. We say that an operator T is *-amenable if the C*-algebra C*(T) generated by T is amenable. In this talk, we will show that the *-amenability of operators is unstable under similarity and each operator similar to T is C*-amenable if and only if T is a polynomially compact operator of order at most two. Moreover, we will show that the set of C*-amenable operators is not closed and nowhere dense in B(H), when . At last, we will discuss the *-amenability of special classes of operators.
Report 26
Reporter: WANG Hang (East China Normal University)
Title: Character identity: A point of view from index theory
Abstract: In this talk, we reconstruct Shelstad's character identities using index theory of elliptic operators in the framework of K-theory, for a pair of real (semisimple, linear, algebraic) groups sharing the same L-group. This geometric interpretation of the character identity reveals that index theory could serve as a new geometric perspective for the algebraic constructions in the Endoscopic transfer appeared in the local Langlands correspondence.
Report 27
Reporter: WANG Kai (Fudan University)
Title: Dixmier trace of quotient module on bounded symmetric domain
Abstract: In this talk, we mainly concern the essential normality of Toeplitz operators on bounded symmetric domains. We define a Hilbert quotient module corresponding to partitions of length 1 and prove that it belongs to the Macaev class Ln,∞. We next obtain an explicit formula for the Dixmier trace of Toeplitz commutators in terms of the underlying boundary geometry. This is a joint work with Prof. Harald Upmeier.
Report 28
Reporter: WANG Maofa (Wuhan University)
Title: Joint Carleson measure and difference of composition operators over the half-plane
Abstract: As is well known joint Carleson measure now is a basic tool to characterize the boundness and compactness of the differences of two composition operators on the weighted Bergman spaces over the unit disk. In this talk, we use Khinchine's inequality and atomic decomposition techniques to introduce similar joint Carleson measure char-acterizations of when the difference of composition operators is bounded or compact from standard weighted Bergman spaces to Lebesgue spaces over the half-plane for all choices of the indexes. As applications, we obtain direct analytic characterizations of the bounded and compact difference of composition operators on such spaces. This talk closes with a joint Carleson measure characterization of when the difference of composition operators is Hilbert-Schmidt. This is a joint work with C. Pang.
Report 29
Reporter: WANG Qin (East China Normal University)
Title: Higher index problems associated with coarse geometry and Banach space geometry
Time: October 28,2017 (Saturday) AM 11:50-12:30
Abstract: Higher index theory associated with coarse geometry is a program to compute K-theory of the Roe C*-algebras of various spaces. There are beautiful links between higher index theory, metric geometry, dynamical systems and Banach space geometry. In this talk, we will discuss these links and some of recent progress in this direction.
Report 30
Reporter: WANG Zipeng (Shaanxi Normal University)
Title: The Doubling Measure Property and Operators on Function Spaces
Abstract: Doubling measures arise naturally in various ways in analysis and geometry and there is an industry building on them. In this talk, we will explain their three applications to operators on function spaces.
(1) Carleson measures on the Bergman and Dirichle space
(2) Weighted inequalities for the Bergman projection
(3) Toeplitz Operators on the weighted harmonic Bergman space.
These are based on my joint works with Cheng Guozheng, Fang Xiang, Guo Kunyu, Yu Jiayang and Zhao Xianfeng.
Report 31
Reporter: WULAN Hasi (Shantou University)
Title: Composition Operators on BMOA and related function spaces
Time: October 28,2017 (Saturday)AM 10:30-11:10
Abstract: I will talk some results on composition operators on BMOA and related function spaces. Also, I will mention some open problems in this area.
Report 32
Reporter: WU Junde (Zhejiang University)
Title: On Quantum Network Theory
Time: October 29,2017 (Sunday) AM 12:00-12:30
Report 33
Reporter: YANG Rongwei (University of New York at Albany)
Title: Hermitian Metrics on Operator Pre - Set Sets
Time: October 29,2017 (Sunday) AM 10:10-10:50
Report 34
Reporter: YAO Xingxing (Wuhan Institute of Technology)
Title: Some Properties of Composition Operators on Dirichlet Series Space
Abstract: In this report, we consider the invariant subspace, complex symmetry, and Toeplitz et al. of the complex operator on the Hilbert space formed by the square sum of the Dirichlet series.
Report 35
Reporter: YU Jiayang (Sichuan University)
Title: Cauchy-Kowalevski And Holmgren Type Theorems with Infinite Number of Variables
Abstract: Firstly, we establish a family of lp induced topologies on and corresponding topologies on with infinity point which will be used to describe analyticity. Secondly, we adapt the definition of analyticity of functions on by Hilbert as monomial expansions and by the method of majorants we get a Cauchy-Kowalevski type theorem with infinite number of variables. Thirdly, based on the Cauchy-Kowalevski type theorem we have established, the tools of abstract Wiener spaces, Malliavin analysis and a divergence theorem for Hilbert space, we obtain a Holmgren type theorem with infinite number of variables.
Report 36
Reporter: ZHANG Jun (Taiyuan University of Technology)
Title: Stronger uncertainty relations with tight bounds
Time: October 28,2017 (Saturday) PM 4:35-5:00
Abstract: The Heisenberg uncertainty principle shows that no one can specify the values of the non-commuting canonically conjugated variables simultaneously. In order to improve the bounds, we utilize quantum superposition principle to establish the upper and lower bounds on the stronger uncertainty relation [Phys. Rev. Lett. 113, 260401 (2014)], i.e., the ``weighted-like” sum of the variances of observables. Our bounds include some free parameters which not only guarantee the nontrivial bounds but also can effectively control the bounds as tightly as one expects. Especially, these parameters don't obviously depend on the state and observables. It also implies one advantage of our method that any nontrivial bound can always be tight enough. In addition, we generalize both bounds to the uncertainty relation with multiple observables, but the perfect tightness is not changed. In addition, we also present tighter bounds on entropic uncertainty relation for multiple measurements in the presence of quantum memory.
Report 37
Reporter: ZHANG Yuanhang(Jilin University)
Title: A problem of Blackadar
Report 38
Reporter: ZHANG Zhitao (Chinese Academy of Sciences)
Title: Existence of solutions for Schrodinger systems with linear and nonlinear couplings
Time: October 28,2017 (Saturday) AM 9:40-10:20
Abstract: We are concerned with the important system of nonlinear Schrodinger equations with linear and nonlinear couplings which arises from Bose-Einstein condensates, we prove phase segregation results of the limit competition case, which covers S. Terracini's conjecture; we use variational methods to prove the existence of ground state and bound state solutions of the systems, and use bifurcation theory to get structure of positive solutions. We give some partial symmetry results of positive solutions by Morse index and obtain existence and uniqueness of positive solution via synchronized solution techniques etc.
Report 39
Reporter: ZHAO Xianfeng (Chongqing University)
Title: The spectrum of Toeplitz operators with some analytic polynomial symbols on the harmonic Bergman space
Time: October 28,2017 (Saturday) PM 5:00-5:25
Abstract: Let p be an analytic polynomial on the unit disk and Tp be the corresponding Toeplitz operator on the harmonic Bergman space. A fundamental but nontrivial problem is to compute the spectrum of a Toeplitz operator. In this talk, we will discuss the structure of the spectrum of Tp via some techniques used in the study of Toeplitz operators on the Bergman space.
