Linear maps preserving equivalence or asymptotic equivalence on Banach space

被引：1

作者：

Qin, Zijie ^{[1
]}

Chen, Lin ^{[1
]}

机构：

[1] Changshu Inst Technol, Sch Math & Stat, Changshu 215500, Peoples R China

来源：

OPEN MATHEMATICS | 2023年 / 21卷 / 01期

关键词：

linear preservers; asymptotic equivalence; equivalence relations; Banach spaces; SIMILARITY;

D O I：

10.1515/math-2023-0125

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let X be a complex Banach space with dimension at least two and B(X) the algebra of all bounded linear operators on X . We show that a bijective linear map Phi preserves asymptotic equivalence if and only if it preserves equivalence, and in turn, if and only if there exist invertible bounded linear operators T and S such that either Phi(A) = TAS Phi or Phi(A) = TA(& lowast;)S for all A is an element of B(X)

引用

页数：8

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