A Representation Theorem for Completely Contractive Dual Banach Algebras

TL;DR

This paper proves that every completely contractive dual Banach algebra can be represented as a $w^*$-closed subalgebra of completely bounded operators on a reflexive operator space, providing a structural characterization.

Contribution

It establishes a representation theorem linking completely contractive dual Banach algebras to operator algebras on reflexive spaces, a novel structural insight.

Findings

Every such algebra is completely isometric to a $w^*$-closed subalgebra

Provides a new operator space framework for dual Banach algebras

Enhances understanding of the structure of dual Banach algebras

Abstract

In this paper, we prove that every completely contractive dual Banach algebra is completely isometric to a $w^\ast$-closed subalgebra the operator space of completely bounded linear operators on some reflexive operator space.