Unitarily invariant norm inequalities for elementary operators involving $G_1$ operators

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.

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

References in corpus (1)

• Gruss inequality for some types of positive linear maps