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报告题目: Cowen-Douglas operators and the third of Halmos' ten problems
报 告 人: 纪奎 教授
报告人所在单位: 河北师范大学
报告日期: 2021-10-22
报告时间: 10:00-11:00
报告地点: 腾讯会议ID: 534 232 190, 密码: 200433
   
报告摘要:

Let T be a bounded linear operator on a complex separable infinite dimensional Hilbert space H. T is called intransitive if it leaves invariant spaces other than 0 or the whole space H; otherwise it is transitive. In 1970, P. R. Halmos raised ten open problems on operator theory. The third problem of Halmos is the following: if an intransitive operator has an inverse, is its inverse also intransitive? In this talk, we introduce some progresses of this problem with the help of Cowen-Douglas operators and spectral analysis.  As the first application, we show that for an invertible hyponormal operator T, if T1 is intransitive and intσ((T1)^) is not connected, then T is also intransitive. As the second application, we show that if T1 has a proper strictly cyclic invariant subspace and there exists a bounded open set Ω which is a connected component of ρ(T1) such that Ω∩U_0=, where U_0 is the connected component of int(σ(T1)^) containing zero point, then T is intransitive. 

10-22海报.pdf

   
本年度学院报告总序号: 246

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