A source of counterexamples in operator theory and how to construct them

DOI10.1016/0024-3795(92)90170-FzbMath0757.15016WikidataQ124843316 ScholiaQ124843316MaRDI QIDQ1187381

Boris Mirman

Publication date: 23 July 1992

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

zbMATH Keywords

Hilbert spacesoperator Lipschitz conditionoperator modulus

Mathematics Subject Classification ID

Norms (inequalities, more than one norm, etc.) of linear operators (47A30) Linear operator inequalities (47A63) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60)

Related Items (1)

Lipschitz-type bounds for the map \(A \to|A|\) on \({\mathcal L}({\mathcal H})\)

Cites Work

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• An estimate of the norm |f(B)-f(A)| for self-adjoint operators A and B
• Spectra of Operators with Fixed Imaginary Parts
• Continuity of the map $S \to \left| S \right|$ for linear operators
• Ten problems in Hilbert space
• Counterexample to a Question on Commutators
• Every n × n Matrix Z with Real Spectrum Satisfies || Z - Z ∗ || ≦ || Z + Z ∗ || (log 2 n + 0.038)

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