Wold-type decomposition for doubly twisted left-invertible covariant representations

TL;DR

This paper introduces a new concept of near-isometric covariant representations of $C^*$-correspondences and establishes their Wold-type decomposition, extending to doubly twisted left-invertible covariant representations of product systems.

Contribution

It presents the first Wold-type decomposition for near-isometric covariant representations and extends this to doubly twisted left-invertible cases in product systems.

Findings

Established Wold-type decomposition for near-isometric covariant representations.

Extended decomposition results to doubly twisted left-invertible covariant representations.

Provided a framework for analyzing covariant representations in $C^*$-correspondences.

Abstract

We will introduce the notion of a near-isometric covariant representation of a $C^*$-correspondence and prove its Wold-type decomposition. Wold-type decomposition for doubly twisted left-invertible covariant representations of a product system is also obtained.