学术报告-许庆祥

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2018-01-22 11:35:00

学术报告

题      目:The polar decomposition for adjointable operators on Hilbert $C^*$-modules and $n$-centered operators ( joint work with Na Liu and Wei Luo from Shanghai Normal University)

报  告  人:许庆祥  教授  (邀请人:邓春源)

                       上海师范大学


时      间:2018-01-22 16:30--17:30

地      点:学院401

报告人简介:

        许庆祥教授,研究方向为泛函分析(算子理论与算子代数)。曾被评为上海市高校优秀青年教师,上海师范大学基础数学硕士点负责人。主要文章发表在国外的J. London Math.Soc.、J. Operator Theory、 SIAM J. Numer. Anal.、SIAM. J. Matrix Anal. Appl.以及国内的《中国科学》(A辑,英文版)等杂志上。


摘      要:

    Abstract: In this talk, we will focus on the polar decomposition for adjointable operators on Hilbert $C^*$-modules and its application in the study of the centered operator. Let $T$ be an adjointable operator between two Hilbert $C^*$-modules and $T^*$ be the adjoint operator of $T$. We will show that $T$ has the polar decomposition if and only if there exists a partial isometry $U$ such that $T=U(T^*T)^frac12$ and $mathcal{R}(U^*)=overline{mathcal{R}(T^*)}$, where $mathcal{R}(U^*)$ and $overline{mathcal{R}(T^*)}$ denote the range of $U^*$ and the norm closure of the range of $T^*$, respectively. Based on this new characterization of the polar decomposition, we will introduce and clarify two types of operators called weakly $n$-centered operators and $n$-centered operators for each natural number $n$. Many results known for bounded
linear operators on Hilbert spaces can then be improved in the general setting of adjointable operators on Hilbert $C^*$-modules