Third Order Trace Formula

TL;DR

This paper provides a new proof for the existence of a third order spectral shift function for self-adjoint operators, extending previous results to unbounded operators bounded below.

Contribution

It introduces an alternative proof for the third order spectral shift function applicable to unbounded self-adjoint operators bounded below.

Findings

Existence of third order spectral shift function established.

Extension to unbounded self-adjoint operators bounded below.

Provides a different proof approach from previous work.

Abstract

In (J. Funct. Anal. 257, 1092-1132 (2009)), Dykema and Skripka showed the existence of higher order spectral shift functions when the unperturbed self-adjoint operator is bounded and the perturbations is Hilbert-Schmidt. In this article, we give a different proof for the existence of spectral shift function for the third order when the unperturbed operator is self-adjoint (bounded or unbounded, but bounded below).