Work

Functions of compact operators under trace class perturbations

Year: 2025

Type: article

Abstract: The paper studies the problem for which continuous functions f f on the real line R \mathbb {R} , the difference of the functions f ( B ) − f ( A ) f(B)-f(A) of compact self-adjoint operators A A and B 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 f is operator Lipschitz on a neighbourhood of zero.

Source: St Petersburg Mathematical Journal

DOI: 10.1090/spmj/1843

Authors: A. Aleksandrov, V. Peller

Institutions: St Petersburg University, St. Petersburg Department of Steklov Institute of Mathematics, Steklov Mathematical Institute

Language: English

Topic: Advanced Banach Space Theory

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Russian Science Foundation

Award: G4208807289