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Structure Theory of Complemented Banach Algebras

Published online by Cambridge University Press:  20 November 2018

Bohdan J. Tomiuk
Bohdan J. Tomiuk*
Affiliation:
University of Ottawa and King's College, University of Durham
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If A is an H*-algebra, then the orthogonal complement of a closed right (left) ideal I is a closed right (left) ideal P. Saworotnow (7) considered Banach algebras which are Hilbert spaces and in which the closed right ideals satisfy the complementation property of an H*-algebra. In our right complemented Banach algebras we drop the requirement of the existence of an inner product and only assume that for every closed right ideal I there is a closed right ideal IP which behaves like the orthogonal complement in a Hilbert space (Definition 1). Thus our algebras may be considered as a generalization of Saworotnow's right complemented algebras.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 14 , 1962 , pp. 651 - 659
Copyright
Copyright © Canadian Mathematical Society 1962

References

1. Bonsall, F. F. and Goldie, A. W., Annihilator algebras, Proc. London Math. Soc. (3), 4 (1954), 154–167.Google Scholar
2. Bonsall, F. F., A minimal property of the norm in some Banach algebras, J. London Math. Soc, 29 (1954), 157–163.Google Scholar
3. Jacobson, N., The radical and semi-simplicity of arbitrary rings, Amer. J. Math., 67 (1945), 300–320.Google Scholar
4. Loomis, L. H., An introduction to abstract harmonic analysis, New York (1953).Google Scholar
5. Kakutani, I. and Mackey, G. W., Ring and lattice characterization of complex Hilbert space, Bull. Amer. Math. Soc. 52 (1946), 727–733.Google Scholar
6. Rickart, C. E., General theory of Banach algebras, New York (1960).Google Scholar
7. Saworotnow, P., On a generalization of the notion of H*-algebra, Proc. Amer. Math. Soc, 8 (1957), 44–55.Google Scholar