Multi-tuple Shilov boundaries of algebra tensor products
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- by Toma V. Tonev PDF
- Proc. Amer. Math. Soc. 113 (1991), 749-753 Request permission
Abstract:
We give a short proof of Basener Slodkowski theorem for multi-tuple Shilov boundaries of tensor products of two uniform algebraas.References
- 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 —, Boundaries for product algebras, preprint, 1975.
- Bruno Kramm, Nuclearity [resp. Schwartzity] helps to embed holomorphic structure into spectra—a survey, Proceedings of the conference on Banach algebras and several complex variables (New Haven, Conn., 1983) Contemp. Math., vol. 32, Amer. Math. Soc., Providence, RI, 1984, pp. 143–162. MR 769503, DOI 10.1090/conm/032/769503
- 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
- Nessim Sibony, Multi-dimensional analytic structure in the spectrum of a uniform algebra, Spaces of analytic functions (Sem. Functional Anal. and Function Theory, Kristiansand, 1975) Lecture Notes in Math., Vol. 512, Springer, Berlin, 1976, pp. 139–165. MR 0632106
- Zbigniew Slodkowski, Analytic multifunctions: $q$-plurisubharmonic functions and uniform algebras, Proceedings of the conference on Banach algebras and several complex variables (New Haven, Conn., 1983) Contemp. Math., vol. 32, Amer. Math. Soc., Providence, RI, 1984, pp. 243–258. MR 769513, DOI 10.1090/conm/032/769513
- Zbigniew Slodkowski, Local maximum property and $q$-plurisubharmonic functions in uniform algebras, J. Math. Anal. Appl. 115 (1986), no. 1, 105–130. MR 835588, DOI 10.1016/0022-247X(86)90027-2
- Edgar Lee Stout, The theory of uniform algebras, Bogden & Quigley, Inc., Publishers, Tarrytown-on-Hudson, N.Y., 1971. MR 0423083
- T. V. Tonev, New relations between Sibony-Basener boundaries, Complex analysis, III (College Park, Md., 1985–86) Lecture Notes in Math., vol. 1277, Springer, Berlin, 1987, pp. 256–262. MR 922339, DOI 10.1007/BFb0078250 —, General complex-analytic structures in uniform algebra spectra, preprint, Sofia, 1987.
- T. Tonev, Multi-dimensional analytic structures and uniform algebras, Several complex variables and complex geometry, Part 2 (Santa Cruz, CA, 1989) Proc. Sympos. Pure Math., vol. 52, Amer. Math. Soc., Providence, RI, 1991, pp. 557–561. MR 1128570
- John Wermer, Banach algebras and several complex variables, 2nd ed., Graduate Texts in Mathematics, No. 35, Springer-Verlag, New York-Heidelberg, 1976. MR 0394218
Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 113 (1991), 749-753
- MSC: Primary 46J20; Secondary 46M05
- DOI: https://doi.org/10.1090/S0002-9939-1991-1057962-6
- MathSciNet review: 1057962