Hilbert modules, rigged modules and stable isomorphism

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.

The paper has been rewritten with emphasis on the theory of non-selfadjoint operator algebras

References in corpus (1)

• The Calculus of One-Sided $M$-Ideals and Multipliers in Operator Spaces