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Proceedings of the American Mathematical Society

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

 
 

 

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