Trace formulas for tuples of commuting contractions

TL;DR

This paper generalizes trace formulas for tuples of commuting contractions, extending previous work to multivariate functions and perturbations within normed ideals, under the condition of dilation to commuting normal contractions.

Contribution

It introduces new trace formulas for multivariate functions of commuting contractions that admit dilation to commuting normal contractions, expanding the scope of prior results.

Findings

Extended trace formulas to multivariate functions of commuting contractions.

Established conditions for perturbations within normed ideals.

Applied dilation techniques to derive new trace identities.

Abstract

This paper extends the trace formulas of [5] with perturbations in normed ideals of $B(H)$ to multivariate functions of commuting contractions admitting a dilation to commuting normal contractions.