Wold decomposition for doubly commuting isometries

TL;DR

This paper extends the classical Wold decomposition to multiple doubly commuting isometries, providing a comprehensive description and generalization of existing results for pairs of such operators.

Contribution

It introduces a several variables analogue of the Wold decomposition specifically for n-tuples of doubly commuting isometries, generalizing prior work on pairs.

Findings

Complete description of n-tuples of doubly commuting isometries

Generalization of Slocinski's Wold-type decomposition

New framework for analyzing multivariable isometries

Abstract

In this paper, we obtain a complete description of the class of n-tuples (n >= 2) of doubly commuting isometries. In particular, we present a several variables analogue of the Wold decomposition for isometries on Hilbert spaces. Our main result is a generalization of M. Slocinski's Wold-type decomposition of a pair of doubly commuting isometries.