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Representation of Banach Algebras with an Involution

Published online by Cambridge University Press:  20 November 2018

J. A. Schatz
J. A. Schatz*
Affiliation:
University of Connecticut
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In 1943 Gelfand and Neumark (3) characterized uniformly closed self-adjoint algebras of bounded operators on a Hilbert space as Banach algebras with an involution (a conjugate linear anti-isomorphism of period two) satisfying several additional conditions. The main purpose of this paper is to point out that if we consider algebras of bounded operators on complex Banach spaces more general than Hilbert space, then we can represent a larger class of algebras by essentially the same methods.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 9 , 1957 , pp. 435 - 442
Copyright
Copyright © Canadian Mathematical Society 1957

References

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