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• W2020600873 abstract "Abstract We study the type decomposition and the rectangular AFD property for W *-TRO’s. Like von Neumann algebras, every W *-TRO can be uniquely decomposed into the direct sum of W *- TRO's of type I , type II , and type III . We may further consider W *-TRO's of type I m,n with cardinal numbers m and n , and consider W *-TRO's of type II λ,μ with λ, μ = 1 or ∞. It is shown that every separable stable W *-TRO (which includes type I ∞, ∞, type II ∞, ∞ and type III ) is TRO-isomorphic to a von Neumann algebra. We also introduce the rectangular version of the approximately finite dimensional property for W *-TRO’s. One of our major results is to show that a separable W *-TRO is injective if and only if it is rectangularly approximately finite dimensional. As a consequence of this result, we show that a dual operator space is injective if and only if its operator predual is a rigid rectangular space (equivalently, a rectangular space)." @default.
• W2020600873 created "2016-06-24" @default.
• W2020600873 creator A5057579746 @default.
• W2020600873 date "2004-08-01" @default.
• W2020600873 modified "2023-09-27" @default.
• W2020600873 title "Type Decomposition and the Rectangular AFD Property for <i>W</i>*-TRO’s" @default.
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• W2020600873 doi "https://doi.org/10.4153/cjm-2004-038-7" @default.
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