DAVIS-WIELANDT SHELLS OF OPERATORS

被引：40

作者：

Li, Chi-Kwong ^{[1
]}

Poon, Yiu-Tung ^{[2
]}

Sze, Nung-Sing ^{[3
]}

机构：

[1] Coll William & Mary, Dept Math, Williamsburg, VA 23185 USA

[2] Iowa State Univ, Dept Math, Ames, IA 50011 USA

[3] Univ Connecticut, Dept Math, Storrs, CT 06269 USA

来源：

OPERATORS AND MATRICES | 2008年 / 2卷 / 03期

关键词：

Davis-Wielandt shells; generalized numerical ranges; spectra; operators;

D O I：

10.7153/oam-02-20

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Basic properties of Davis-Wielandt shells are presented. Conditions on two operators A and B with the same Davis-Wielandt shells are analyzed. Special attention is given to the case when B is a compression of A, and when B = A*, A(t), or (A*)(t), where A(t) is the transpose of A with respect to an orthonormal basis. The results are used to study the point spectrum, approximate point spectrum, and residual spectrum of the sum of two operators. Relation between the geometrical properties of the Davis-Wielandt shells and algebraic properties of operators are obtained. Complete descriptions of the Davis-Wielandt shells are given for several classes of operators.

引用

页码：341 / 355

页数：15

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