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arXiv · 1610.03869

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

Fuad Kittaneh·Mohammad Sal Moslehian·Mohammad Sababheh
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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.

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Fuad Kittaneh, Mohammad Sal Moslehian, Mohammad Sababheh. 2016-10-12. Unitarily invariant norm inequalities for elementary operators involving $G_{1}$ operators. https://arxiv.org/abs/1610.03869

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