On a generalization of W*-modules

TL;DR

This paper introduces new results on a generalized class of modules over dual operator algebras, extending the theory of W*-modules and Hilbert spaces.

Contribution

It provides several novel theoretical results on modules that generalize W*-modules over dual operator algebras.

Findings

New properties of generalized W*-modules

Extensions of Riesz representation theorem analogues

Deeper understanding of module structures over dual operator algebras

Abstract

In a recent paper of the first author and Kashyap, a new class of modules over dual operator algebras is introduced. These generalize the W*-modules (that is, Hilbert C*-modules over a von Neumann algebra which satisfy an analogue of the Riesz representation theorem for Hilbert spaces), which in turn generalize the theory of Hilbert spaces. In the present paper we give several new results about these modules.