The q-commuting contractions and $*$-regular dilations

TL;DR

This paper introduces $*$-regular dilations for q-commuting contractions, extending previous results on commuting contractions to a broader non-commutative setting.

Contribution

It generalizes the concept of dilations to q-commuting tuples, expanding the theoretical framework beyond classical commuting contractions.

Findings

Defined $*$-regular dilation for q-commuting tuples

Extended Gaspar-Suciu and Timotin's results to non-commutative cases

Provided new theoretical insights into operator dilations

Abstract

We introduce the notion of $*$-regular dilation for q-commuting tuples of contractions and generalize the results due to Gaspar-Suciu and Timotin on commuting contractions.