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On Normed Algebras which Satisfy a Reality Condition

Published online by Cambridge University Press:  20 November 2018

Silvio Aurora
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Various results exist which permit real Banach algebras satisfying some sort of “reality condition” to be identified with the algebra of all continuous real-valued functions on a suitable compact space (or with the algebra of all continuous real-valued functions that * Vanish at infinity“ on a suitable non-compact, locally compact space in case the algebra has no unit). (Terminology follows (4), so that compact and locally compact spaces must be Hausdorff spaces, in addition to satisfying the usual requirements.) Kadison established such a result in (6, Theorem 6.6) for any Banach algebra with unit, if the algebra satisfies an appropriate reality condition and has a norm N such that N(x)2 — N(x2) for all x.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 13 , 1961 , pp. 675 - 682
Copyright
Copyright © Canadian Mathematical Society 1961

References

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