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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

$ C\sp*$-algebras isomorphic after tensoring


Author: Joan Plastiras
Journal: Proc. Amer. Math. Soc. 66 (1977), 276-278
MSC: Primary 46L05; Secondary 46M05
MathSciNet review: 0461158
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Abstract: It is always true that whenever $ \mathfrak{A}$ and $ \mathfrak{B}$ are isomorphic $ {C^\ast}$-algebras then $ {\mathfrak{M}_2} \otimes \mathfrak{A}$ and $ {\mathfrak{M}_2} \otimes \mathfrak{B}$ are also isomorphic, and the converse holds for many standard examples. In this note we present two $ {C^\ast}$-algebras $ \mathfrak{A}$ and $ \mathfrak{B}$ such that $ {\mathfrak{M}_2} \otimes \mathfrak{A}$ and $ {\mathfrak{M}_2} \otimes \mathfrak{B}$ are isomorphic whereas $ \mathfrak{A}$ and $ \mathfrak{B}$ are not.


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DOI: https://doi.org/10.1090/S0002-9939-1977-0461158-9
Keywords: $ {C^\ast}$-algebra, isomorphism, compact operators, essential commutant, matrix units, Hilbert space
Article copyright: © Copyright 1977 American Mathematical Society