Norm inequality for the class of self-adjoint absolute value generalized derivations
It is shown that for \(0\leq \alpha\leq \frac{2}{3}\) and for \(A,{\mathcal B},X \in{\mathcal B}(H)\) (\({\mathcal B}(H)\) is the algebra of bounded operators on a Hilbert space \(H\)) the following inequality holds NEWLINE\[NEWLINE \parallel A ^\alpha X-X B ^\alpha \parallel \leq 2^{2-\alpha} \parallel X\parallel^{1-\alpha} \parallel AX-XB \parallel^\alpha. .NEWLINE\]
scientific article; zbMATH DE number 1677964