Doubly commuting and dual doubly commuting semigroups of isometries

TL;DR

This paper investigates the structure of semigroups of isometries that commute under specific conditions such as double commutativity or dual double commutativity, revealing their algebraic properties.

Contribution

It characterizes the structure of doubly commuting and dual doubly commuting semigroups of isometries, providing new insights into their algebraic organization.

Findings

Structures of doubly commuting semigroups of isometries are characterized.

Structures of dual doubly commuting semigroups of isometries are characterized.

The paper establishes foundational properties under additional commutativity assumptions.

Abstract

Structures of commuting semigroups of isometries under certain additional assumptions like double commutativity or dual double commutativity are found.