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• W2023198539 abstract "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 be eliminated. Recent progress of the author with Effros and Zarikian now enables weak*-versions of these characterization theorems. For example, we prove a result analogous to Sakai's famous characterization of von Neumann algebras as the C *-algebras with predual, namely, that the σ -weakly closed unital (not-necessarily-selfadjoint) subalgebras of B ( H ) for a Hilbert space H , are exactly the unital operator algebras which possess an operator space predual. This removes one of the hypotheses from an earlier characterization due to Le Merdy. We also show that the multiplier operator algebras of dual operator spaces are dual operator algebras. Using this we refine several known results characterizing dual operator modules." @default.
• W2023198539 created "2016-06-24" @default.
• W2023198539 creator A5015708217 @default.
• W2023198539 date "2001-07-01" @default.
• W2023198539 modified "2023-09-30" @default.
• W2023198539 title "Multipliers and Dual Operator Algebras" @default.
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• W2023198539 doi "https://doi.org/10.1006/jfan.2001.3759" @default.
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