2013/09/14 by N. Christopher Phillips, Phillips, N. Christopher
Mathematics · #47L10 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebra over a field #Algebra representation #Algebraic structures and combinatorial models #Computer science #Crystal structure #Diagonal #FOS: Mathematics #Functional Analysis (math.FA) #Geometry #Isomorphism (crystallography) #Mathematics #Nest algebra #Non-associative algebra #Primary 46H20 #Pure mathematics #Secondary 46H05 #Tensor (intrinsic definition) #Tensor product #Ultra high frequency #math.FA #msc:46H05 #msc:46H20 #msc:47L10
paper · pdf · doi:10.48550/arxiv.1309.3694
AMSLaTeX; 42 pages. New in Version 2: Lemma 3.8 and Corollary 3.9, for use in the proof of what is now Lemma 3.10
openalex publication_date 2013/09/14 · arxiv created 2013/09/25 · arxiv updated 2013/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
In a previous paper, we introduced Lp UHF algebras for p in [1, ∞). We concentrated on the spatial Lp UHF algebras, which are classified up to isometric isomorphism by p and the scaled ordered K0-group. In this paper, we concentrate on a larger class, the Lp UHF algebras of tensor product type constructed using diagonal similarities. Such an algebra is still simple and has the same K-theory as the corresponding spatial Lp UHF algebra. For each choice of p and the K-theory, we provide uncountably many nonisomorphic such algebras. We further characterize the spatial algebras among them. In particular, if A is one of these algebras, then A is isomorphic (not necessarily isometrically) to a spatial Lp UHF algebra if and only if A is amenable as a Banach algebra, also if and only if A has approximately inner tensor flip. These conditions are also equivalent to a natural numerical condition defined in terms of the ingredients used to construct the algebra.