Column and row operator spaces over QSL_p-spaces and their use in abstract harmonic analysis

TL;DR

This paper extends the concepts of column and row operator spaces to quotients of subspaces of Lp-spaces, providing new operator space structures for Banach algebras in harmonic analysis to enhance understanding.

Contribution

It introduces canonical operator space structures on Banach algebras in harmonic analysis using quotients of Lp-spaces, enabling new analytical insights.

Findings

Banach algebras gain canonical operator space structures

Operator space structures become completely bounded

New insights into harmonic analysis algebras

Abstract

The notions of column and row operator space were extended by A. Lambert from Hilbert spaces to general Banach spaces. In this paper, we use column and row spaces over quotients of subspaces of general $L_p$-spaces to equip several Banach algebras occurring naturally in abstract harmonic analysis with canonical, yet not obvious operator space structures that turn them into completely bounded Banach algebras. We use these operator space structures to gain new insights on those algebras.