Isomorphic classification of $\ast$-algebras of log-integrable functions

TL;DR

This paper establishes necessary and sufficient conditions for when two $ ext{*}$-algebras of log-integrable functions are $ ext{*}$-isomorphic, using the concept of passport of a normed Boolean algebra.

Contribution

It introduces a new criterion based on passport of normed Boolean algebras for classifying $ ext{*}$-algebras of log-integrable functions up to isomorphism.

Findings

Derived necessary and sufficient conditions for $ ext{*}$-isomorphism.

Connected algebraic isomorphism with Boolean algebra passports.

Provided a classification framework for $ ext{*}$-algebras of log-integrable functions.

Abstract

Using the notion of passport of a normed Boolean algebra, necessary and sufficient conditions for a $\ast$-isomorphism of $\ast$-algebras of log-integrable measurable functions are found.