Near inclusions of amenable operator algebras

TL;DR

This paper demonstrates that amenable operator algebras that are nearly contained in complemented dual operator algebras can be embedded into them through a similarity transformation, utilizing Johnson's theorem on approximate multiplicativity.

Contribution

It establishes a new embedding result for amenable operator algebras in dual operator algebras using approximate multiplicative maps.

Findings

Amenable operator algebras can be embedded into dual operator algebras via similarity.

The proof uses Johnson's theorem on approximately multiplicative maps.

Near containment implies embeddability in this context.

Abstract

We prove that if an amenable operator algebra is nearly contained in a complemented dual operator algebra, then it can be embedded inside this dual operator algebra via a similarity. The proof relies on a B.E. Johnson Theorem on approximately multiplicative maps.