Title : ( Maps preserving some spectral domains of operator products )
Authors: Sepide Hajighasemi Azghandi , Shirin Hejazian ,
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Abstract
Let X be an infinite-dimensional Banach space and let B(X) denote the algebra of all bounded linear operators on X. For T ∈ B(X) the sets σ_1(T)={λ ∈ σ(T) | T−λI is a semi-Fredholm operator}, σ_2(T) = {λ ∈ σ(T) | T − λI is a Fredholm operator}, and σ_3(T) = {λ ∈ σ(T) | T − λI is a Weyl operator} are called, respectively, the semi-Fredholm domain, the Fredholm domain, and the Weyl domain of T in the spectrum, σ(T). We characterize surjective maps on B(X) (with no additivity assumption) leaving invariant σ_i(TS) or σ_i(TST) for all T, S ∈ B(X) and i ∈ {1, 2, 3}.
Keywords
, Linear operator; semi, Fredholm domain; Fredholm domain; Weyl domain; preserver map
@article{paperid:1081786,
author = {Hajighasemi Azghandi, Sepide and Hejazian, Shirin},
title = {Maps preserving some spectral domains of operator products},
journal = {Linear and Multilinear Algebra},
year = {2020},
volume = {70},
number = {12},
month = {August},
issn = {0308-1087},
pages = {2367--2381},
numpages = {14},
keywords = {Linear operator; semi-Fredholm domain; Fredholm domain; Weyl domain; preserver map},
}
%0 Journal Article
%T Maps preserving some spectral domains of operator products
%A Hajighasemi Azghandi, Sepide
%A Hejazian, Shirin
%J Linear and Multilinear Algebra
%@ 0308-1087
%D 2020
