Hostname: page-component-6bf8c574d5-xtvcr Total loading time: 0 Render date: 2025-02-24T03:01:37.290Z Has data issue: false hasContentIssue false
  • English
  • Français

Ring Isomorphisms of Banach Algebras

Published online by Cambridge University Press:  20 November 2018

Irving Kaplansky
Irving Kaplansky*
Affiliation:
University of Chicago
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.

In discussing an isomorphism between two Banach algebras, one will ordinarily tacitly assume that the mapping is linear (i.e., preserves the complex scalars as well as the ring operations). In general this cannot be avoided; for instance if the two Banach algebras are just the field of complex numbers, then the isomorphism is unrestricted, and could be given by any one of the myriads of discontinuous automorphisms of the complex numbers.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 6 , 1954 , pp. 374 - 381
Copyright
Copyright © Canadian Mathematical Society 1954

References

1. Arnold, B. H., Rings of operators on vector spaces, Ann. of Math., 45 (1944), 24–49.Google Scholar
2. Feldman, C., The Wedderburn principal theorem in Banach algebras, Proc. Amer. Math. Soc, 2 (1951), 771–777.Google Scholar
3. Jacobson, N., Structure theory of simple rings without finiteness assumptions, Trans. Amer. Math. Soc, 57 (1945), 228–245.Google Scholar
4. Jacobson, N., On the theory of primitive rings, Ann. of Math., 48 (1947), 8–21.Google Scholar
5. Kakutani, S. and Mackey, G. W., Ring and lattice characterizations of complex Hilbert space, Bull. Amer. Math. Soc, 52 (1946), 727–733.Google Scholar
6. Kaplansky, I., Locally compact rings III, Amer. J. of Math., 74 (1952), 929–935.Google Scholar
7. Rickart, C. E., Representation of certain Banach algebras on Hilbert space, Duke Math. J., 18 (1951), 27–39.Google Scholar