Morita Type Equivalences and Reflexive Algebras
نویسنده
چکیده
Two unital dual operator algebras A,B are called ∆-equivalent if there exists an equivalence functor F : AM → BM which “extends” to a ∗−functor implementing an equivalence between the categories ADM and BDM. Here AM denotes the category of normal representations of A and ADM denotes the category with the same objects as AM and ∆(A)-module maps as morphisms (∆(A) = A ∩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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