An Ando-type dilation on right LCM monoids

TL;DR

This paper proves a new dilation theorem for pairs of commuting contractions combined with right LCM monoid representations, extending previous results to broader algebraic structures.

Contribution

It introduces an Ando-type dilation theorem for right LCM monoids, generalizing earlier work to include Cartesian and free product representations.

Findings

Pairs of commuting contractions with monoid representations can be dilated to commuting isometries.

The dilation extends to an isometric monoid representation under certain regularity conditions.

The results generalize existing theorems to more complex algebraic structures.

Abstract

We establish an Ando-type dilation theorem for a pair of commuting contractions together with a representation of a right LCM monoid via either the Cartesian or the free product. We prove that if each individual contraction together with the monoid representation has $*$-regular dilation, then they can be dilated to commuting isometries and an isometric representation of the monoid. This extends an earlier result of Barik and Das.