算子理论与算子代数及其应用报告会

报告题目：Generalized Cauchy singular integral operators on the unit circle

报告人：桑元琦 博士 （西南财经大学）

报告时间：2022年08月26日（星期五）下午：15：00-16：00

报告地点：腾讯视频会议（线上）

会议ID：213-721-412 会议密码：220826

校内联系人：刘超 （博士后）

报告摘要：In this talk, we relate generalized Cauchy singular integral operators to a number of operators, including Cauchy singular integral operators, (dual) truncated Toeplitz operators, the dilation of truncated Toeplitz operators, Foguel-Hankel operators, $2\times 2$ block Toeplitz operators, Toeplitz plus Hankel operators etc. We establish the short exact sequences associated of the $C^{*}-$algebras generated by generalized Cauchy singular integral operators with bounded or quasi-continuous symbols. As a consequence we obtain the spectra of various classes of generalized Cauchy singular integral operators, the spectral inclusion theorem and calculate its Fredholm index. Moreover, we give the necessary and sufficient conditions for invertibility (Fredholmness) of generalized Cauchy singular integral operators via Wiener-Hopf factorization.

报告人简介：桑元琦，西南财经大学讲师，博士毕业于重庆大学，主要研究模型空间相关的算子理论问题。主持完成中国博士后基金1项，参与国家自然科学基金项目3项。研究成果发表于《Results Math.》，《Banach J. Math. Anal.》，《J. Math. Anal. Appl.》,《Oper. Matrices.》,《Ann. Funct. Anal.》等。