Unitarily invariant norm inequalities for elementary operators involving $G_{1}$ operators

Fuad Kittaneh; Mohammad Sal Moslehian; Mohammad Sababheh

Unitarily invariant norm inequalities for elementary operators involving $G_{1}$ operators

Functional Analysis 2017-09-26 v1 Operator Algebras

Authors: Fuad Kittaneh , Mohammad Sal Moslehian , Mohammad Sababheh

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

operator theory numerical range bergman spaces

Cite

@article{arxiv.1610.03869,
  title  = {Unitarily invariant norm inequalities for elementary operators involving $G_{1}$ operators},
  author = {Fuad Kittaneh and Mohammad Sal Moslehian and Mohammad Sababheh},
  journal= {arXiv preprint arXiv:1610.03869},
  year   = {2017}
}

Comments

11 pages; to appear in Linear Algebra Appl. (LAA)

Unitarily invariant norm inequalities for elementary operators involving $G_{1}$ operators

Abstract

Keywords

Cite

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