Krein's trace formula for unitary operators and operator Lipschitz functions (English translation)

TL;DR

This paper characterizes the class of functions on the unit circle for which Krein's trace formula applies to pairs of unitary operators with trace class difference, establishing their equivalence with operator Lipschitz functions.

Contribution

It provides a complete description of the function space where Krein's trace formula is valid for unitary operators, linking it to operator Lipschitz functions.

Findings

The space of functions satisfying Krein's trace formula coincides with operator Lipschitz functions.

The result applies to arbitrary pairs of unitary operators with trace class difference.

The paper clarifies the functional framework for trace formulas in operator theory.

Abstract

The main result of this paper is a description of the space of functions on the unit circle, for which Krein's trace formula holds for arbitrary pairs of unitary operators with trace class difference. This space coincides with the space of operator Lipschitz functions on the unit circle.