$C^*$-algebras isomorphic after tensoring
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- by Joan Plastiras PDF
- Proc. Amer. Math. Soc. 66 (1977), 276-278 Request permission
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.References
- William Arveson, An invitation to $C^*$-algebras, Graduate Texts in Mathematics, No. 39, Springer-Verlag, New York-Heidelberg, 1976. MR 0512360, DOI 10.1007/978-1-4612-6371-5
- Horst Behncke and Horst Leptin, $C^*$-algebras with a two-point dual, J. Functional Analysis 10 (1972), 330–335. MR 0399874, DOI 10.1016/0022-1236(72)90031-6
- James G. Glimm, On a certain class of operator algebras, Trans. Amer. Math. Soc. 95 (1960), 318–340. MR 112057, DOI 10.1090/S0002-9947-1960-0112057-5
- Joan K. Plastiras, Compact perturbations of certain von Neumann algebras, Trans. Amer. Math. Soc. 234 (1977), no. 2, 561–577. MR 458241, DOI 10.1090/S0002-9947-1977-0458241-5
Additional Information
- © Copyright 1977 American Mathematical Society
- 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