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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Joint spectra and analytic set-valued functions


Author: M. Klimek
Journal: Trans. Amer. Math. Soc. 294 (1986), 187-196
MSC: Primary 46H30; Secondary 32F15, 47A10
MathSciNet review: 819942
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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.


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DOI: https://doi.org/10.1090/S0002-9947-1986-0819942-5
Article copyright: © Copyright 1986 American Mathematical Society