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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Maximal $ C\sp{\ast} $-subalgebras of a Banach algebra


Author: Ellen Torrance
Journal: Proc. Amer. Math. Soc. 25 (1970), 622-624
MSC: Primary 46.65
MathSciNet review: 0259629
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Abstract: Let $ A$ be a complex Banach algebra with identity and let $ H$ be its set of hermitain elements. It is shown that $ H + iH$ is a $ {C^{\ast}}$-algebra if and only if $ {h^2} \in H + iH$ whenever $ h \in H$; and that every $ {C^{\ast}}$-subalgebra of $ A$ is contained in $ H + iH$.


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DOI: https://doi.org/10.1090/S0002-9939-1970-0259629-7
Keywords: $ {C^{\ast}}$-algebra, hermitian element of $ B$-algebra, semi-innerproduct, $ {C^{\ast}}$-subalgebra
Article copyright: © Copyright 1970 American Mathematical Society