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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

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