Morita Transforms of Tensor Algebras

2010/07/20 by Paul S. Muhly, Muhly, Paul S., Baruch Solel +1
Mathematics · #47L30 #47L55 #47L65 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Primary: 46H25 #Rings and Algebras (math.RA) #Secondary: 46H25

paper · pdf · doi:10.48550/arxiv.1007.3486

openalex publication_date 2010/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that if M and N are C^*-algebras and if E (resp. F) is a C^*-correspondence over M (resp. N), then a Morita equivalence between (E,M) and (F,N) implements a isometric functor between the categories of Hilbert modules over the tensor algebras of T₊(E) and T₊(F). We show that this functor maps absolutely continuous Hilbert modules to absolutely continuous Hilbert modules and provides a new interpretation of Popescu's reconstruction operator.

Citations

• Morita equivalence for c∗-algebras and w∗-algebras

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