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Real rank of tensor products of $ C\sp \ast$-algebras


Authors: Kazunori Kodaka and Hiroyuki Osaka
Journal: Proc. Amer. Math. Soc. 123 (1995), 2213-2215
MSC: Primary 46L85; Secondary 46L05, 46M05
DOI: https://doi.org/10.1090/S0002-9939-1995-1264820-4
MathSciNet review: 1264820
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Abstract: We study the real rank of tensor products of $ {C^ \ast }$-algebras. From the dimension theory: $ \dim (X \times Y) \leq \dim X + \dim Y$, it is naturally hoped that $ RR(A \otimes B) \leq RR(A) + RR(B)$. We then prove that it is false generally. Moreover, we point out that (FS)-property for $ {C^ \ast }$-algebras is not stable under taking tensor products.


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DOI: https://doi.org/10.1090/S0002-9939-1995-1264820-4
Article copyright: © Copyright 1995 American Mathematical Society

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