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Strictly real Banach algebras

Published online by Cambridge University Press:  17 April 2009

John Boris Miller
John Boris Miller
Affiliation:
Department of Mathematics, Monash University Clayton, Victoria 3168, Australia
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A complex Banach algebra is a complexification of a real Banach algebra if and only if it carries a conjugation operator. We prove a uniqueness theorem concerning strictly real selfconjugate subalgebras of a given complex algebra. An example is given of a complex Banach algebra carrying two distinct but commuting conjugations, whose selfconjugate subalgebras are both strictly real. The class of strictly real Banach algebras is shown to be a variety, and the manner of their generation by suitable elements is proved. A corollary describes some strictly real subalgebras in Hermitian Banach star algebras, including C* algebras.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 47 , Issue 3 , June 1993 , pp. 505 - 519
Copyright
Copyright © Australian Mathematical Society 1993

References

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