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MULTIPLICATIVE SPECTRAL FUNCTIONALS ON $C(X)$
Published online by Cambridge University Press: 08 January 2020
Abstract
If $A$ is a commutative $C^{\star }$-algebra and if $\unicode[STIX]{x1D719}:A\rightarrow \mathbb{C}$ is a continuous multiplicative functional such that $\unicode[STIX]{x1D719}(x)$ belongs to the spectrum of $x$ for each $x\in A$, then $\unicode[STIX]{x1D719}$ is linear and hence a character of $A$. This establishes a multiplicative Gleason–Kahane–Żelazko theorem for $C(X)$.
MSC classification
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 102 , Issue 2 , October 2020 , pp. 303 - 307
- Copyright
- © 2020 Australian Mathematical Publishing Association Inc.
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