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 | References | Similar Articles | Additional Information
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