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Proceedings of the American Mathematical Society

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

 
 

 

$C^*$-algebras isomorphic after tensoring


Author: Joan Plastiras
Journal: Proc. Amer. Math. Soc. 66 (1977), 276-278
MSC: Primary 46L05; Secondary 46M05
DOI: https://doi.org/10.1090/S0002-9939-1977-0461158-9
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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Keywords: <IMG WIDTH="31" HEIGHT="21" ALIGN="BOTTOM" BORDER="0" SRC="images/img3.gif" ALT="${C^\ast }$">-algebra, isomorphism, compact operators, essential commutant, matrix units, Hilbert space
Article copyright: © Copyright 1977 American Mathematical Society