Hilbert $C^*$-modules over $\Sigma^*$-algebras II: $\Sigma^*$-Morita equivalence

Clifford A. Bearden

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arXiv · 1701.08333

Hilbert $C^$-modules over $\Sigma^$-algebras II: $\Sigma^*$-Morita equivalence

Clifford A. Bearden

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Abstract

In previous work, we defined and studied $\Sigma^*$-modules, a class of Hilbert $C^*$-modules over $\Sigma^*$-algebras (the latter are $C^*$-algebras that are sequentially closed in the weak operator topology). The present work continues this study by developing the appropriate $\Sigma^*$-algebraic analogue of the notion of strong Morita equivalence for $C^*$-algebras. We define strong $\Sigma^*$-Morita equivalence, prove a few characterizations, look at the relationship with equivalence of categories of a certain type of Hilbert space representation, study $\Sigma^*$-versions of the interior and exterior tensor products, and prove a $\Sigma^*$-version of the Brown-Green-Rieffel stable isomorphism theorem.

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BibTeX RIS

Clifford A. Bearden. 2017-01-28. Hilbert $C^*$-modules over $\Sigma^*$-algebras II: $\Sigma^*$-Morita equivalence. https://arxiv.org/abs/1701.08333

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