Maximal ideal space of a commutative coefficient algebra

TL;DR

This paper characterizes the maximal ideal space of the smallest coefficient C*-algebra generated by a commutative algebra and a partial isometry, expanding understanding of their structural properties.

Contribution

It provides a description of the maximal ideal space for the coefficient algebra associated with a pair (A,U) involving a commutative C*-algebra and a partial isometry.

Findings

Describes the structure of the maximal ideal space

Identifies conditions for the algebra's properties

Advances the theory of coefficient algebras in operator theory

Abstract

The basic notion of the article is a pair (A,U), where A is a commutative C*-algebra and U is a partial isometry such that mapping U()U* is an endomorphism of A and U*U belongs to A. We give a description of the maximal ideal space of the smallest coefficient C*-algebra of the algebra C*(A,U) generated by the system (A,U).