Besov spaces in operator theory

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 ${\mathrm{\ell }}^1$ and ${\mathrm{\ell }}^{\mathrm{\infty }}$. An essential part of the survey is devoted to the role of Besov spaces in various problems of perturbation theory when studying the behavior of functions of a single operator or of a collection of operators under their perturbation.