Rigged modules II: multipliers and duality

TL;DR

This paper extends the theory of rigged modules to include multipliers and duality, providing new results on their structure and tensor products within operator algebra theory.

Contribution

It introduces new results on rigged and weak*-rigged modules, including an Eilenberg-Watts type theorem, advancing the understanding of their duality and tensor products.

Findings

New theorems on rigged modules and their tensor products

An Eilenberg-Watts type theorem for weak*-rigged modules

Enhanced understanding of duality in nonselfadjoint operator algebras

Abstract

In a previous paper with Kashyap we generalized the theory of $W^*$-modules to the setting of modules over nonselfadjoint dual operator algebras, obtaining the class of weak*-rigged modules. The present paper and its contemporaneous predecessor comprise the sequel which we promised at that time would be forthcoming. We give many new results about rigged and weak*-rigged modules and their tensor products, such as an Eilenberg-Watts type theorem.