Higher order spectral shift for contractions

TL;DR

This paper establishes strong Schatten norm estimates for operator derivatives along contraction paths and uses these results to prove the existence of higher order spectral shift functions for pairs of contractions.

Contribution

It introduces new Schatten norm estimates for derivatives of contractions and demonstrates their application in spectral shift function theory.

Findings

Established strong Schatten norm estimates for operator derivatives.

Proved existence of higher order spectral shift functions for contraction pairs.

Applied estimates to spectral theory of contractions.

Abstract

We derive strong estimates for Schatten norms of operator derivatives along paths of contractions and apply them to prove existence of higher order spectral shift functions for pairs of contractions.