Reflexivity of operator algebras of finite split strict multiplicity

TL;DR

This paper investigates the structure of abelian operator algebras with finite split strict multiplicity, providing conditions under which these algebras are reflexive or hereditarily reflexive, thus advancing understanding of their invariant subspaces.

Contribution

It introduces new sufficient conditions for the reflexivity and hereditary reflexivity of abelian operator algebras with finite split strict multiplicity.

Findings

Identifies conditions ensuring reflexivity of these algebras

Establishes criteria for hereditary reflexivity

Enhances understanding of invariant subspace structure

Abstract

We study the invariant subspaces of abelian operator algebras of finite split strict multiplicity. We give sufficient conditions for the reflexivity and hereditary reflexivity of these algebras.