$C^*$-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
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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.
- William Arveson, An invitation to $C^ *$-algebras, Springer-Verlag, New York-Heidelberg, 1976. Graduate Texts in Mathematics, No. 39. MR 0512360
- Horst Behncke and Horst Leptin, $C^ *$-algebras with a two-point dual, J. Functional Analysis 10 (1972), 330–335. MR 0399874, DOI https://doi.org/10.1016/0022-1236%2872%2990031-6
- James G. Glimm, On a certain class of operator algebras, Trans. Amer. Math. Soc. 95 (1960), 318–340. MR 112057, DOI https://doi.org/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 https://doi.org/10.1090/S0002-9947-1977-0458241-5
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46L05, 46M05
Retrieve articles in all journals with MSC: 46L05, 46M05
Additional Information
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