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Subhomogeneous AF $ C\sp \ast$-algebras and their Fubini products. II


Author: Seung-Hyeok Kye
Journal: Proc. Amer. Math. Soc. 97 (1986), 244-246
MSC: Primary 46L05
DOI: https://doi.org/10.1090/S0002-9939-1986-0835873-4
MathSciNet review: 835873
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Abstract: If $ C$ is a nuclear $ {C^*}$-subalgebra of a $ {C^*}$-algebra $ A$, then we have $ C \otimes D = (A \otimes D) \cap (C \otimes B)$ for any $ {C^*}$-algebras $ B$ and $ D$ with $ D \subset B$. Using this, we show that if $ A$ and $ B$ are AF algebras and $ A{ \otimes _F}B = A \otimes B$, then either $ A$ or $ B$ must be subhomogeneous.


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DOI: https://doi.org/10.1090/S0002-9939-1986-0835873-4
Keywords: Subhomogeneous AF $ {C^*}$-algebras, Fubini products of $ {C^*}$-algebras, intersection results for $ {C^*}$-tensor products
Article copyright: © Copyright 1986 American Mathematical Society

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