A Morita type equivalence for dual operator algebras |
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Authors: | GK Eleftherakis |
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Institution: | Department of Mathematics, University of Athens, Panepistimioupolis 157 84, Athens, Greece |
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Abstract: | We generalize the main theorem of Rieffel for Morita equivalence of W∗-algebras to the case of unital dual operator algebras: two unital dual operator algebras A,B have completely isometric normal representations α,β such that α(A)=M∗β(B)M]−w∗ and β(B)=Mα(A)M∗]−w∗ for a ternary ring of operators M (i.e. a linear space M such that MM∗M⊂M) if and only if there exists an equivalence functor which “extends” to a ∗-functor implementing an equivalence between the categories and . By we denote the category of normal representations of A and by the category with the same objects as and Δ(A)-module maps as morphisms (Δ(A)=A∩A∗). We prove that this functor is equivalent to a functor “generated” by a B,A bimodule, and that it is normal and completely isometric. |
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Keywords: | 47L30 16D90 46M15 47L45 47L55 |
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