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Functions of compact operators under trace class perturbations

A. B. Aleksandrov, V. V. Peller

Abstract

The paper studies the problem, for which continuous functions $f$ on the real line ${\Bbb R}$, the difference of the functions $f(B)-f(A)$ of self-adjoint operators $A$ and $B$ with trace class difference must also be of trace class. The main result of the paper shows that this happens if and only if the function $f$ is operator Lipschitz on a neighbourhood of zero.

Functions of compact operators under trace class perturbations

Abstract

The paper studies the problem, for which continuous functions on the real line , the difference of the functions of self-adjoint operators and with trace class difference must also be of trace class. The main result of the paper shows that this happens if and only if the function is operator Lipschitz on a neighbourhood of zero.
Paper Structure (4 sections, 32 equations)

This paper contains 4 sections, 32 equations.

Table of Contents

  1. Introduction
  2. Basic definitions
  3. The main result
  4. Normal operators with trace class difference