Completely co-bounded Schur multipliers

TL;DR

This paper investigates the properties of completely co-bounded Schur multipliers on operator spaces, including $B(ell_2)$ and Schatten classes, and explores Herz-Schur multipliers on groups, providing new insights into their structure.

Contribution

It introduces simple results characterizing completely co-bounded Schur multipliers and extends the analysis to Herz-Schur multipliers on groups, offering novel theoretical insights.

Findings

Characterization of completely co-bounded Schur multipliers

Results on Schur multipliers on $B(ell_2)$ and Schatten classes

Analysis of Herz-Schur multipliers on groups

Abstract

A linear map $u\colon \ E\to F$ between operator spaces is called completely co-bounded if it is completely bounded as a map from $E$ to the opposite of $F$. We give several simple results about completely co-bounded Schur multipliers on $B(\ell_2)$ and the Schatten class $S_p$. We also consider Herz-Schur multipliers on groups.