Joint spectra and analytic set-valued functions
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Abstract:
We investigate analyticity of joint spectra of ${A^m}$-valued holomorphic mappings, where $A$ denotes a complex Banach algebra. We show also that if $K$ is an analytic set-valued function whose values are compact subsets of ${{\mathbf {C}}^n}$ and $d$ is the transfinite diameter in ${{\mathbf {C}}^n}$, then the upper-semicontinuous regularization of $\log d(K)$ is plurisubharmonic. Moreover, we give higher dimensional extensions of Aupetit’s Scarcity Theorem.References
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Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 294 (1986), 187-196
- MSC: Primary 46H30; Secondary 32F15, 47A10
- DOI: https://doi.org/10.1090/S0002-9947-1986-0819942-5
- MathSciNet review: 819942