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Proceedings of the American Mathematical Society

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

 

 

An elementary proof of Słodkowski's theorem


Author: Enrico Casadio Tarabusi
Journal: Proc. Amer. Math. Soc. 99 (1987), 783-784
MSC: Primary 46H05
DOI: https://doi.org/10.1090/S0002-9939-1987-0877057-0
MathSciNet review: 877057
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Abstract: Let $ \mathfrak{A}$ be a complex Banach algebra, and $ \sigma (x)$ be the spectrum of $ x \in \mathfrak{A}$. We give a very short proof that if $ f:G \to \mathfrak{A}$ is holomorphic ($ G$ open in $ {\mathbf{C}}$), then $ \sigma \circ f:G \to {2^{\mathbf{C}}}$ is Oka-analytic.


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DOI: https://doi.org/10.1090/S0002-9939-1987-0877057-0
Keywords: Analytic multifunction, spectrum, Banach algebras
Article copyright: © Copyright 1987 American Mathematical Society