Order and Spectrum Preserving Maps on Positive Operators

被引：9

作者：

Semrl, Peter ^{[1
]}

机构：

[1] Univ Ljubljana, Fac Math & Phys, Jadranska 19, SI-1000 Ljubljana, Slovenia

来源：

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES | 2017年 / 69卷 / 06期

关键词：

spectrum preserver; order preserver; positive operator; SPACE EFFECT ALGEBRAS; MAXIMAL-IDEALS; LINEAR-MAPS; AUTOMORPHISMS;

D O I：

10.4153/CJM-2016-039-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We describe the general form of surjective maps on the cone of all positive operators that preserve order and spectrum. The result is optimal as shown by counterexamples. As an easy consequence, we characterize surjective order and spectrum preserving maps on the set of all selfadjoint operators.

引用

页码：1422 / 1435

页数：14

共 17 条

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Aupetit B, 1998, BANACH ALGEBRAS '97, P55

[2] An extension of the Gleason-Kahane-Zelazko theorem: A possible approach to Kaplansky's problem [J].