Hankel operators in the perturbation theory of unitary and self-adjoint operators

DOI10.1007/BF01078390zbMath0587.47016OpenAlexW2033086316MaRDI QIDQ1072077

Vladimir V. Peller

Publication date: 1985

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01078390

zbMATH Keywords

spectral shift functionmetric properties of some Hankel operatorsoperator integralsperturbation theory of unitary and self-adjoint operatorsrepresentation of the trace

Mathematics Subject Classification ID

Perturbation theory of linear operators (47A55) Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35)

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Cites Work

• An estimate of the norm |f(B)-f(A)| for self-adjoint operators A and B
• Remarks on the spectral shift function
• Schur multipliers
• Absolutely summing operators in $ℒ_{p}$-spaces and their applications
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