A Morita theorem for dual operator algebras
نویسندگان
چکیده
منابع مشابه
A Morita Theorem for Dual Operator Algebras
We prove that two dual operator algebras are weak Morita equivalent in the sense of [4] if and only if they have equivalent categories of dual operator modules via completely contractive functors which are also weakcontinuous on appropriate morphism spaces. Moreover, in a fashion similar to the operator algebra case we can characterize such functors as the module normal Haagerup tensor product ...
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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) = [Mβ(B)M] ∗ and β(B) = [Mα(A)M] ∗ for a ternary ring of operators M (i.e. a linear space M such that MMM ⊂ M) if and only if there exists an equivalence functor F ...
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We prove that two unital dual operator algebras A,B are stably isomorphic if and only if they are ∆-equivalent [7], if and only if they have completely isometric normal representations α, β on Hilbert spaces H,K respectively and there exists a ternary ring of operators M ⊂ B(H,K) such that α(A) = [M∗β(B)M]−w and β(B) = [Mα(A)M∗]−w .
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In a previous paper we showed how the main theorems characterizing operator algebras and operator modules, fit neatly into the framework of the ‘noncommutative Shilov boundary’, and more particularly via the left multiplier operator algebra of an operator space. As well as giving new characterization theorems, the approach of that paper allowed many of the hypotheses of the earlier theorems to ...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2009
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2009.02.014