$\lambda$-tensor product of operator spaces

TL;DR

This paper introduces a new $mbda$-tensor product framework for operator spaces, extending existing theories like the operator space projective and Schur tensor products to unify and generalize their structures.

Contribution

It develops a novel $mbda$-tensor product theory that broadens the scope of tensor products in operator space theory, connecting previous models into a unified framework.

Findings

Defines the $mbda$-tensor product for operator spaces

Extends the operator space projective tensor product theory

Generalizes the Schur tensor product for operator spaces

Abstract

We propose a theory of $\lambda$-tensor product of operator spaces which extends the theory of Blecher-Paulsen and Effros-Ruan for the operator space projective tensor product \cite{blecp}, \cite{effros}, \cite{eff} and that of Rajpal-Kumar-Itoh for the Schur tensor product \cite{vandee4} of operator spaces.