Hilbert modules, rigged modules and stable isomorphism

TL;DR

This paper characterizes rigged modules over operator algebras that are orthogonally complemented in an infinite column space, revealing their role as bimodules of Morita equivalence between stably isomorphic algebras.

Contribution

It provides a characterization of certain rigged modules as Morita equivalence bimodules within the framework of operator algebras.

Findings

Rigged modules orthogonally complemented in $C_ abla( ext{A})$ are characterized.

Such modules serve as Morita equivalence bimodules.

The work extends the understanding of module structures in operator algebra theory.

Abstract

Rigged modules over an operator algebra are a generalization of Hilbert modules over a $C^{\star}$-algebra. We characterize the rigged modules over an operator algebra $\mathcal A$ which are orthogonally complemented in $C_\infty(\mathcal A),$ the space of infinite columns with entries in $\mathcal A.$ We show that every such rigged module `restricts' to a bimodule of Morita equivalence between appropriate stably isomorphic operator algebras.