Higher-order spectral shift for pairs of contractions via multiplicative path

TL;DR

This paper extends the spectral shift theory to higher orders for pairs of contractions and dissipative operators using multiplicative paths, building on previous trace formula work.

Contribution

It proves the existence of higher-order spectral shift functions for these operator pairs, adapting methods from prior trace formula research.

Findings

Established higher-order spectral shift functions for contractions.

Extended spectral shift theory to dissipative operators.

Built upon and adapted previous trace formula techniques.

Abstract

In \cite{Mor}, Marcantognini and Mor\'{a}n obtained Koplienko-Neidhardt trace formula for pairs of contractions and pairs of maximal dissipative operators via multiplicative path. In this article, we prove the existence of higher-order spectral shift functions for pairs of contractions and pairs of maximal dissipative operators via multiplicative path by adapting the argument employed in \cite{Mor}.