The Davis-Wielandt Shell of linear Operators

：刘浏（大连理工大学）
：2025-08-28 11:00
：海韵园实验楼S105

报告人：刘浏（大连理工大学）

时  间：2025年8月28日11:00

地  点：海韵园实验楼S105

内容摘要:

We introduce the concept of Davis-Wielandt Shell for an unbounded linear operator, which is a generalization of the numerical range. Give the relationships between the spectrum and the Davis-Wielandt Shell. The spectral inclusions for the sum and product of two linear operators are derived by utilizing the Davis-Wielandt Shells. Moreover, we list some resolvent estimates based on the DW shell, overcoming the limitation that resolvent estimates induced by the numerical range may be invalid for certain points in the resolvent set. We show that the upper bounds for norms of resolvents maybe tighter than those obtained from the numerical range, together with some sharp inequalities that improve some existing inequalities involving the numerical radius. Also, we geive descriptions of the DW-shell for some composition operators on the Hardy space.

个人简介：

刘浏，大连理工大学数学科学学院教授，博士生导师，主要从事算子理论、算子代数及其在控制理论中的应用研究，在Syst. Control. Lett., IMA J. Math Control等期刊发表论文30余篇，入选辽宁省“兴辽英才”青年拔尖、辽宁省百千万人才工程，大连市科技之星。

 

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