Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-1977-0461158-9
MathSciNet review: 0461158
Full-text PDF

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.


References [Enhancements On Off] (What's this?)

  • [1] W. Arveson, An invitation to $ {C^\ast}$-algebras, Springer-Verlag, Berlin and New York, 1976. MR 0512360 (58:23621)
  • [2] H. Behncke and H. Leptin, $ {C^\ast}$-algebras with a two-point dual, J. Functional Analysis 10 (1972), 330-335. MR 0399874 (53:3716)
  • [3] J. Glimm, On a certain class of operator algebras, Trans. Amer. Math. Soc. 95 (1960), 318-340. MR 0112057 (22:2915)
  • [4] J. Plastiras, Compact perturbations of certain von Neumann algebras, Trans. Amer. Math. Soc. (to appear). MR 0458241 (56:16444)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46L05, 46M05

Retrieve articles in all journals with MSC: 46L05, 46M05


Additional Information

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

American Mathematical Society