【系列报告】Amenability, similarity and approximation

2017-10-25



天津市数学会系列报告

(第一讲)




报告题目:Amenability, similarity and approximation


报告人: 石洛宜副教授 (天津工业大学


摘要: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*-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 dim(H)=\infty. At last, we will discuss the *-amenability of special classes of operators.



报告时间:20171031日(星期二)下午1600-1700


报告地点: 第二报告厅



欢迎各位老师和同学参加!!


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