On subharmonicity of the capacity of the spectrum
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- by Zbigniew Słodkowski PDF
- Proc. Amer. Math. Soc. 81 (1981), 243-249 Request permission
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).References
- Bernard Aupetit, Propriétés spectrales des algèbres de Banach, Lecture Notes in Mathematics, vol. 735, Springer, Berlin, 1979 (French). MR 549769, DOI 10.1007/BFb0064204 Z. Slodkowski, Analytic set-valued functions and spectra (in preparation)
- Richard F. Basener, A generalized Shilov boundary and analytic structure, Proc. Amer. Math. Soc. 47 (1975), 98–104. MR 352990, DOI 10.1090/S0002-9939-1975-0352990-9
- Arlen Brown and R. G. Douglas, On maximum theorems for analytic operator functions, Acta Sci. Math. (Szeged) 26 (1965), 325–327. MR 213912
- A. T. Dash and M. Schechter, Tensor products and joint spectra, Israel J. Math. 8 (1970), 191–193. MR 261377, DOI 10.1007/BF02771314
- Donna Kumagai, Subharmonic functions and uniform algebras, Proc. Amer. Math. Soc. 78 (1980), no. 1, 23–29. MR 548077, DOI 10.1090/S0002-9939-1980-0548077-4
- Charles E. Rickart, General theory of Banach algebras, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR 0115101
- Zbigniew Słodkowski, Wojciech Wojtyński, and Jaroslav Zemánek, A note on quasinilpotent elements of a Banach algebra, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 25 (1977), no. 2, 131–134 (English, with Russian summary). MR 438124
- M. Tsuji, Potential theory in modern function theory, Maruzen Co. Ltd., Tokyo, 1959. MR 0114894
- Edoardo Vesentini, On the subharmonicity of the spectral radius, Boll. Un. Mat. Ital. (4) 1 (1968), 427–429 (English, with Italian summary). MR 0244766
- John Wermer, Subharmonicity and hulls, Pacific J. Math. 58 (1975), no. 1, 283–290. MR 393567, DOI 10.2140/pjm.1975.58.283
- Wiesław Żelazko, Banach algebras, Elsevier Publishing Co., Amsterdam-London-New York; PWN—Polish Scientific Publishers, Warsaw, 1973. Translated from the Polish by Marcin E. Kuczma. MR 0448079
- Vasiliĭ Sergeevič Vladimirov, Methods of the theory of functions of many complex variables, The M.I.T. Press, Cambridge, Mass.-London, 1966. Translated from the Russian by Scripta Technica, Inc; Translation edited by Leon Ehrenpreis. MR 0201669
Additional Information
- © Copyright 1981 American Mathematical Society
- 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