Morita Type Equivalences and Reflexive Algebras

Details Morita Type Equivalences and Reflexive Algebras Morita Type Equivalences and Reflexive Algebras

2007-09-05

arxiv.org/abs/0709.0600v1

Mathematics

Operator Algebras

Scientific paper

Two unital operator algebras A, B are called Delta-equivalent if there exists an equivalence functor between the categories A-mod and B-mod which "extends" to a *-functor implementing an equivalence between the categories A-dmod and B-dmod. Here A-mod denotes the category of normal representations of A and A-dmod denotes the category with the same objects as A-mod and D(A)-module maps (D(A) is the diagonal of A). We prove that any such functor maps completely isometric representations to completely isometric representations, "respects" the lattices of the algebras and maps reflexive algebras to reflexive algebras. We present applications to the class of CSL algebras.

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