Theory of q-commuting contractions : joint reducing subspaces and orthogonal decompositions

TL;DR

This paper extends canonical decomposition results from commuting contractions to Q-commuting contractions, focusing on joint reducing subspaces and orthogonal decompositions when Q is a family of unitaries.

Contribution

It generalizes existing theories of contraction decompositions to the broader setting of Q-commuting contractions with unitary Q operators.

Findings

Established canonical decompositions for Q-commuting contractions.

Extended results to doubly Q-commuting contractions.

Provided new insights into joint reducing subspaces for these operators.

Abstract

In the literature, we have several results associated with canonical decomposition of commuting contractions. In this paper, we generalize a few of these results to $Q$-commuting contractions. Here we mainly deal with $Q$-commuting and doubly $Q$-commuting contractions when $Q$ is a family of unitary operators.