Operator Algebras with Unique Preduals

TL;DR

This paper proves that certain operator algebras, specifically free semigroup algebras and some containing dense compact operators, have a unique Banach space predual, simplifying previous proofs.

Contribution

It establishes the uniqueness of the Banach space predual for free semigroup algebras and provides a new, simpler proof for a class of operator algebras with dense compact subalgebras.

Findings

Free semigroup algebras have a unique Banach space predual.

Weak*-closed unital operator algebras with dense compact subalgebras also have a unique predual.

Simplified proof techniques for predual uniqueness.

Abstract

We show that every free semigroup algebras has a (strongly) unique Banach space predual. We also provide a new simpler proof that a weak*-closed unital operator operator algebra containing a weak* dense subalgebra of compact operators has a unique Banach space predual.