$L^p$-modules and $L^p$-correspondences

TL;DR

This paper develops an $L^p$-operator algebra framework analogous to Hilbert C*-modules, introducing $L^p$-modules, morphisms, and tensor products to expand the theory of operator modules beyond the C*-algebra setting.

Contribution

It introduces the concept of $L^p$-modules and $L^p$-correspondences, extending the theory of Hilbert C*-modules to the $L^p$-operator algebra context.

Findings

Defined concrete $L^p$-modules and their morphisms

Established basic constructions including direct sums and tensor products

Formulated the theory of $L^p$-correspondences and their tensor products

Abstract

We introduce an $L^p$-operator algebraic analogue of Hilbert C*- modules. We present the theory of concrete $L^p$-modules, their morphisms, and basic constructions including countable direct sums and tensor products. We then define $L^p$-correspondences and the interior tensor product of these.