Hilbert modules, rigged modules and stable isomorphism

2021/06/09 by George Eleftherakis, G. K. Eleftherakis, Eleftherakis, G. K. +2
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Holomorphic and Operator Theory #math.OA

paper · pdf · doi:10.48550/arxiv.2106.04882

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

arxiv created 2021/08/31 · arxiv updated 2021/09/01

Abstract

Rigged modules over an operator algebra are a generalization of Hilbert modules over a C^⋆-algebra. We characterize the rigged modules over an operator algebra \mathcal A which are orthogonally complemented in C_∞(\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.

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