The Lifshitz–Krein trace formula and operator Lipschitz functions

DOI10.1090/proc/13140zbMath1353.47023arXiv1601.00490OpenAlexW2963338367MaRDI QIDQ2827370

Vladimir V. Peller

Publication date: 19 October 2016

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1601.00490

Mathematics Subject Classification ID

Linear operators belonging to operator ideals (nuclear, (p)-summing, in the Schatten-von Neumann classes, etc.) (47B10) Hermitian and normal operators (spectral measures, functional calculus, etc.) (47B15) Functional calculus for linear operators (47A60) Perturbation theory of linear operators (47A55) Linear symmetric and selfadjoint operators (unbounded) (47B25) Transformers, preservers (linear operators on spaces of linear operators) (47B49)

Related Items (15)

Bernstein functions of several semigroup generators on Banach spaces under bounded perturbations, II ⋮ Bernstein functions of several semigroup generators on Banach spaces under bounded perturbations ⋮ Analytic operator Lipschitz functions in the disk and a trace formula for functions of contractions ⋮ A functional calculus of closed operators on Banach space. III: Certain topics of perturbation theory ⋮ Higher-order spectral shift for pairs of contractions via multiplicative path ⋮ Absolute continuity of spectral shift ⋮ HIGHER ORDER DIFFERENTIABILITY OF OPERATOR FUNCTIONS IN SCHATTEN NORMS ⋮ Higher order \(\mathcal{S}^2\)-differentiability and application to Koplienko trace formula ⋮ The Koplienko-Neidhardt trace formula for unitaries -- a new proof ⋮ Krein's trace formula for unitary operators and operator Lipschitz functions ⋮ A trace formula for functions of contractions and analytic operator Lipschitz functions ⋮ On a trace formula for functions of noncommuting operators ⋮ On a generalization of an approximation operator defined by A. Guessab ⋮ Lifshitz-Kreĭn trace formula for Hirsch functional calculus on Banach spaces ⋮ Trace singularities in obstacle scattering and the Poisson relation for the relative trace

Cites Work

• Multiple operator integrals in perturbation theory
• Operator Hölder-Zygmund functions
• Hankel operators in the perturbation theory of unitary and self-adjoint operators
• Tensor product of a finite number of spectral measures is always a spectral measure
• The range of a normal derivation
• Operator Lipschitz functions
• Continuity of the map $S \to \left| S \right|$ for linear operators
• Operator smoothness in Schatten norms for functions of several variables: Lipschitz conditions, differentiability and unbounded derivations
• CLASSES OF OPERATOR-SMOOTH FUNCTIONS. I. OPERATOR-LIPSCHITZ FUNCTIONS
• Counterexample to a Question on Commutators
• Similarity problems and completely bounded maps. Includes the solution to ``The Halmos problem.
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