An elementary proof of Słodkowski’s theorem
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- by Enrico Casadio Tarabusi
- Proc. Amer. Math. Soc. 99 (1987), 783-784
- DOI: https://doi.org/10.1090/S0002-9939-1987-0877057-0
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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.References
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- Zbigniew Słodkowski, Analytic set-valued functions and spectra, Math. Ann. 256 (1981), no. 3, 363–386. MR 626955, DOI 10.1007/BF01679703
Bibliographic Information
- © Copyright 1987 American Mathematical Society
- 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