MAPS PRESERVING THE SPECTRUM OF SKEW LIE PRODUCT OF OPERATORS

被引：2

作者：

Alzedan, Eman ^{[1
]}

Mabrouk, Mohamed ^{[2
]}

机构：

[1] Umm Al Qura Univ, Dept Math, Fac Appl Sci, Mecca 21955, Saudi Arabia

[2] Fac Sci Sfax, Dept Math, Sfax, Tunisia

来源：

KRAGUJEVAC JOURNAL OF MATHEMATICS | 2022年 / 46卷 / 04期

关键词：

Nonlinear preservers; spectrum; Skew Lie product; PERIPHERAL SPECTRUM; BANACH-ALGEBRAS;

D O I：

10.46793/KgJMat2204.525A

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let B(H) denote the algebra of all bounded linear operators acting on a complex Hilbert space H. In this paper, we show that a surjective map phi on B(H) satisfies sigma(phi(T)phi(S) - phi(S)phi(T)*) = sigma(TS - ST*), T, S is an element of B(H), if and only if there exists a unitary operator U is an element of B(H) such that phi(T) = lambda UTU*, T is an element of B(H), where lambda is an element of {-1, 1}.

引用

页码：525 / 532

页数：8

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