Simplified proof of the Theorem of Varopoulos in the commutative case

TL;DR

This paper provides a simplified proof of the Theorem of Varopoulos for commutative Banach *-algebras by analyzing the continuity of bitraces using the Closed Graph Theorem.

Contribution

It introduces a streamlined proof of the Varopoulos theorem in the commutative setting through continuity properties of bitraces.

Findings

Simplified proof of the Varopoulos theorem in the commutative case.

Establishment of continuity properties of bitraces on Banach *-algebras.

Application of the Closed Graph Theorem to the proof.

Abstract

We give continuity properties of bitraces on (possibly non-commutative) Banach *-algebras based on the Closed Graph Theorem, leading to a simplified proof of the Theorem of Varopoulos in the commutative case.