Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-25T18:21:51.021Z Has data issue: false hasContentIssue false
  • English
  • Français

Modular Annihilator, A*-Algebras

Published online by Cambridge University Press:  20 November 2018

B. J. Tomiuk
B. J. Tomiuk*
Affiliation:
University of Ottawa, Ottawa, Ontario
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We find several equivalent conditions for an A*-algebra with dense socle to be completely continuous. Such an A*-algebra is modular annihilator [10]. We also study modular annihilator A*-algebras with the weak (βk)-property and obtain a necessary and sufficient condition for such algebras to be dual.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 15 , Issue 3 , September 1972 , pp. 421 - 426
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Barnes, B. A., Subalgebras of modular annihilator algebras, Proc. Cambridge Philos. Soc. 66 (1969), 5-12.Google Scholar
2. Barnes, B. A., Modular annihilator algebras, Canad. J. Math. 18 (1966), 566-578.Google Scholar
3. Barnes, B. A., Algebras with spectral expansion property, Illinois J. Math. 11 (1967), 284-290.Google Scholar
4. Barnes, B. A., On the existence of minimal ideals in a Banach algebra, Trans. Amer. Math. Soc. 133 (1968), 511-517.Google Scholar
5. Bonsall, F. F. and Goldie, A. W., Annihilator algebras, Proc. London Math. Soc. 14 (1954), 154-167.Google Scholar
6. Kaplansky, I., The structure of certain operator algebras, Trans. Amer. Math. Soc. 70 (1951), 219-255.Google Scholar
7. T. Ogasawara and Yoshinaga, K., Weakly completely continuous Banach*-algebras, J. Sci. Hiroshima Univ. Ser. A18 (1954), 15-36.Google Scholar
8. Rickart, C. E., General Theory of Banach algebras, Van Nostrand, Princeton, N.J. 1960.Google Scholar
9. Tomiuk, B. J. and Wong, P. K., Annihilator and complemented Banach*-algebras, J. Austral. Math. Soc. 13 (1971), 47-66.Google Scholar
10. Yood, B., Ideals in topological rings, Canad. J. Math. 16 (1964), 28-45.Google Scholar