On the Grothendieck Theorem for jointly completely bounded bilinear forms

TL;DR

This paper revises the proof of the Grothendieck Theorem for jointly completely bounded bilinear forms on C*-algebras, making it more algebraic by using Cuntz algebras and establishing that Blecher's inequality constant exceeds one.

Contribution

It provides a C*-algebraic modification of the Grothendieck Theorem proof and determines the strict inequality of Blecher's inequality constant.

Findings

Proof method is essentially C*-algebraic using Cuntz algebras

The best constant in Blecher's inequality is strictly greater than one

Enhanced understanding of bilinear forms on C*-algebras

Abstract

We show how the proof of the Grothendieck Theorem for jointly completely bounded bilinear forms on C*-algebras by Haagerup and Musat can be modified in such a way that the method of proof is essentially C*-algebraic. To this purpose, we use Cuntz algebras rather than type III factors. Furthermore, we show that the best constant in Blecher's inequality is strictly greater than one.