Maximal 𝐶*-subalgebras of a Banach algebra

Torrance, Ellen

doi:10.1090/S0002-9939-1970-0259629-7

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

Proc. Amer. Math. Soc. 25 (1970), 622-624

DOI: https://doi.org/10.1090/S0002-9939-1970-0259629-7

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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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