Norm inequality for the class of self-adjoint absolute value generalized derivations (Q2757719)
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scientific article; zbMATH DE number 1677964
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Norm inequality for the class of self-adjoint absolute value generalized derivations |
scientific article; zbMATH DE number 1677964 |
Statements
28 November 2001
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singular values
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three line theorem for operators
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unitarily invariant norms
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Norm inequality for the class of self-adjoint absolute value generalized derivations (English)
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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\[NEWLINE \parallel A ^\alpha X-X B ^\alpha \parallel \leq 2^{2-\alpha} \parallel X\parallel^{1-\alpha} \parallel AX-XB \parallel^\alpha. .NEWLINE\]
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