Schur tensor product of operator spaces

TL;DR

This paper systematically investigates the schur tensor product within the frameworks of operator spaces and C*-algebras, providing foundational insights into its properties and applications.

Contribution

It introduces a comprehensive analysis of the schur tensor product in operator spaces and C*-algebras, expanding understanding of its structure and potential uses.

Findings

Established fundamental properties of the schur tensor product.

Connected the schur tensor product to existing tensor product theories.

Provided new tools for analyzing operator spaces and C*-algebras.

Abstract

We develop a systematic study of the schur tensor product both in the category of operator spaces and in that of $C^*$-algebras.