Topologies on the quasi-spectrum of a $C^{\ast }$-algebra
Author:
Wai Mee Ching
Journal:
Proc. Amer. Math. Soc. 46 (1974), 273-276
MSC:
Primary 46L05
DOI:
https://doi.org/10.1090/S0002-9939-1974-0367668-4
MathSciNet review:
0367668
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: We study two topologies, the Gelfand topology and the Jacobson topology, on the quasi-spectrum of a ${C^ \ast }$-algebra. We prove that the Gelfand topology is finer than the Jacobson topology.
- Jacques Dixmier, Les $C^{\ast } $-algèbres et leurs représentations, Cahiers Scientifiques, Fasc. XXIX, Gauthier-Villars & Cie, Éditeur-Imprimeur, Paris, 1964 (French). MR 0171173
- Irving Kaplansky, The structure of certain operator algebras, Trans. Amer. Math. Soc. 70 (1951), 219–255. MR 42066, DOI https://doi.org/10.1090/S0002-9947-1951-0042066-0
- John von Neumann, Continuous geometry, Princeton Mathematical Series, No. 25, Princeton University Press, Princeton, N.J., 1960. Foreword by Israel Halperin. MR 0120174
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46L05
Retrieve articles in all journals with MSC: 46L05
Additional Information
Keywords:
Quasi-spectrum,
<!– MATH ${C^ \ast }$ –> <IMG WIDTH="31" HEIGHT="21" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="${C^ \ast }$">-algebra,
algebraic spectrum,
Jacobson topology,
Gelfand topology
Article copyright:
© Copyright 1974
American Mathematical Society
