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- W3044187568 abstract "We define spatial [Formula: see text] AF algebras for [Formula: see text], and prove the following analog of the Elliott AF algebra classification theorem. If [Formula: see text] and [Formula: see text] are spatial [Formula: see text] AF algebras, then the following are equivalent: [Formula: see text] and [Formula: see text] have isomorphic scaled preordered [Formula: see text]-groups. [Formula: see text] as rings. [Formula: see text] (not necessarily isometrically) as Banach algebras. [Formula: see text] is isometrically isomorphic to [Formula: see text] as Banach algebras. [Formula: see text] is completely isometrically isomorphic to [Formula: see text] as matricial [Formula: see text] operator algebras. As background, we develop the theory of matricial [Formula: see text] operator algebras, and show that there is a unique way to make a spatial [Formula: see text] AF algebra into a matricial [Formula: see text] operator algebra. We also show that any countable scaled Riesz group can be realized as the scaled preordered [Formula: see text]-group of a spatial [Formula: see text] AF algebra." @default.
- W3044187568 created "2020-07-29" @default.
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- W3044187568 date "2020-12-01" @default.
- W3044187568 modified "2023-09-28" @default.
- W3044187568 title "Classification of spatial Lp AF algebras" @default.
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- W3044187568 doi "https://doi.org/10.1142/s0129167x20500883" @default.
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