Linear Algebra and its Applications, ( ISI ), Volume (513), No (2), Year (2017-1) , Pages (84-95)

#### Title : ( Unitarily invariant norm inequalities for elementary operators involving G_{1} operators )

Citation: BibTeX | EndNote

#### Abstract

In this paper, motivated by perturbation theory of operators, we present some upper bounds for $|||f(A)Xg(B)+ X|||$ in terms of $|||\,|AXB|+|X|\,|||$ and $|||f(A)Xg(B)- X|||$ in terms of $|||\,|AX|+|XB|\,|||$, where $A, B$ are $G_{1}$ operators, $|||\cdot|||$ is a unitarily invariant norm and $f, g$ are certain analytic functions. Further, we find some new upper bounds for the the Schatten $2$-norm of $f(A)X\pm Xg(B)$. Several special cases are discussed as well.

#### Keywords

$G_{1}$ operator; unitarily invariant norm; elementary operator; perturbation; analytic function
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@article{paperid:1059195,
title = {Unitarily invariant norm inequalities for elementary operators involving G_{1} operators},
journal = {Linear Algebra and its Applications},
year = {2017},
volume = {513},
number = {2},
month = {January},
issn = {0024-3795},
pages = {84--95},
numpages = {11},
keywords = {$G_{1}$ operator; unitarily invariant norm; elementary operator; perturbation; analytic function},
}