Multipliers on Noncommutative Orlicz Spaces

TL;DR

This paper develops general criteria for multiplication operators between noncommutative Orlicz spaces, compares them with classical $L^p$-space results, and explores their compactness properties.

Contribution

It introduces broad criteria for the existence of multipliers on noncommutative Orlicz spaces and analyzes their differences from $L^p$-space theory.

Findings

Criteria encompass existing results

Differences from $L^p$-space multiplier theory identified

Compactness properties of operators characterized

Abstract

We establish very general criteria for the existence of multiplication operators between noncommutative Orlicz spaces $L^{\psi_0}(\tM)$ and $L^{\psi_1}(\tM)$. We then show that these criteria contain existing results, before going on to briefly look at the extent to which the theory of multipliers on Orlicz spaces differs from that of $L^p$-spaces. In closing we describe the compactness properties of such operators.