Besov spaces in operator theory

V. V. Peller

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 79 (2024) no. 1, pp. 1-52

Résumé

The survey is devoted to diverse applications of Besov classes in operator theory. It is illustrated how Besov classes are used to describe Hankel operators of Schatten–von Neumann classes; various applications of this description are considered. Next, we discuss the role of Besov classes in norm estimates of polynomials of power bounded operators on Hilbert space and related estimates of Hankel matrices in tensor products of the spaces $\ell^1$ and $\ell^\infty$. An essential part of the survey is devoted to the role of Besov spaces in various problems of perturbation theory, in studies of the behaviour of functions of a single operator or a collection of operators under their perturbation. Bibliography: 107 titles.

Détail

Keywords: Hankel operators, Schatten–von Neumann classes, power bounded operators, projective tensor products, injective tensor products, perturbations of linear operators, self-adjoint operators, double operator integrals, triple operator integrals.
Mots-clés : Besov spaces, Schur multipliers

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