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)
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页数：8
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