On the maximality of subdiagonal algebras

TL;DR

This paper addresses Arveson's problem by establishing conditions under which a subdiagonal algebra is maximal, specifically when it remains invariant under the modular group of a faithful normal state preserved by its conditional expectation.

Contribution

It proves that a subdiagonal algebra is maximal if invariant under the modular group of a faithful normal state preserved by its conditional expectation.

Findings

Subdiagonal algebra is maximal under certain invariance conditions.

Invariance under the modular group implies maximality.

Provides a solution to Arveson's problem in this context.

Abstract

We consider Arveson's problem on the maximality of subdiagonal algebras. We prove that a subdiagonal algebra is maximal if it is invariant under the modular group of a faithful normal state which is preserved by the conditional expectation associated with the subdiagonal algebra.