On a generalization of Ando's dilation theorem

TL;DR

This paper generalizes Ando's dilation theorem by introducing $Q$-commuting operators, extending the classical theory to a broader class of operator relations with new dilation and lifting results.

Contribution

It introduces $Q$-commuting operators and proves a generalized commutant lifting theorem and dilation theorem for this new class.

Findings

Established a generalized Ando's dilation theorem for $Q$-commuting operators.

Extended the classical commutant lifting theorem to the $Q$-commuting setting.

Provided new tools for analyzing operator relations beyond commuting operators.

Abstract

We introduce the notion of $Q$-commuting operators which is a generalization of commuting operators. We prove a generalized version of commutant lifting theorem and Ando's dilation theorem in the context of $Q$-commuting operators.