Positivity of spectral shift functions and infinite-dimensional BMV conjecture

TL;DR

This paper proves the BMV conjecture for trace-class perturbations of semi-bounded operators and confirms the positivity of higher order spectral shift functions in a broad operator setting.

Contribution

It provides a solution to the BMV conjecture for a class of unbounded operators and establishes positivity results for spectral shift functions under Schatten--von Neumann perturbations.

Findings

Confirmed the BMV conjecture for trace-class perturbations.

Established positivity of higher order spectral shift functions.

Extended results to unbounded self-adjoint operators.

Abstract

We obtain a solution to the Bessis-Moussa-Villani conjecture for a trace-class perturbation of a semi-bounded operator and answer affirmatively the question on positivity of higher order spectral shift functions in the setting of Schatten--von Neumann perturbations of (possibly unbounded) self-adjoint operators.