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Proceedings of the American Mathematical Society

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

 

 

On subharmonicity of the capacity of the spectrum


Author: Zbigniew Słodkowski
Journal: Proc. Amer. Math. Soc. 81 (1981), 243-249
MSC: Primary 46J10; Secondary 47A55
DOI: https://doi.org/10.1090/S0002-9939-1981-0593466-6
MathSciNet review: 593466
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Abstract: It is shown that if $ {T_\lambda }$ is an analytic operator valued function (or if $ f$, $ g$ belong to a uniform algebra $ A$) then $ n$th diameters and logarithmic capacity of $ \sigma ({T_\lambda })$ (or of the set $ g({f^{ - 1}}(\lambda ))$) are subharmonic functions of $ \lambda $ (on a suitable domain).


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0593466-6
Keywords: Spectrum, Shilov boundary, subharmonic functions, logarithmic capacity
Article copyright: © Copyright 1981 American Mathematical Society