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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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


Author: Ellen Torrance
Journal: Proc. Amer. Math. Soc. 25 (1970), 622-624
MSC: Primary 46.65
DOI: https://doi.org/10.1090/S0002-9939-1970-0259629-7
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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Keywords: <!– MATH ${C^{\ast }}$ –> <IMG WIDTH="31" HEIGHT="21" ALIGN="BOTTOM" BORDER="0" SRC="images/img2.gif" ALT="${C^{\ast }}$">-algebra, hermitian element of <IMG WIDTH="22" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$B$">-algebra, semi-innerproduct, <!– MATH ${C^{\ast }}$ –> <IMG WIDTH="31" HEIGHT="21" ALIGN="BOTTOM" BORDER="0" SRC="images/img17.gif" ALT="${C^{\ast }}$">-subalgebra
Article copyright: © Copyright 1970 American Mathematical Society