Polynomial hulls with convex sections and interpolating spaces
Author:
Zbigniew Slodkowski
Journal:
Proc. Amer. Math. Soc. 96 (1986), 255-260
MSC:
Primary 32E20; Secondary 46E99, 46M35
DOI:
https://doi.org/10.1090/S0002-9939-1986-0818455-X
MathSciNet review:
818455
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: Assume that is compact and has convex vertical sections. Denote by
its polynomially convex hull. It is shown that
, if nonempty, can be covered by graphs of analytic functions
. The proof is based on complex interpolation theory for families of finite-dimensional normed spaces.
- [1] H. Alexander and J. Wermer, On the approximation of singularity sets by analytic varieties, Pacific J. Math. 104 (1983), 263-268. MR 684289 (84e:32016)
- [2] -, Polynomial hulls with convex fibers, Math. Ann. 27 (1985), 99-109. MR 779607 (86i:32025)
- [3] B. Aupetit, Analytic multivalued functions in Banach algebras, Adv. in Math. 44 (1982), 18-60. MR 654547 (84b:46059)
- [4] R. Coifman, M. Gwikel, R. Rochberg, Y. Sagher and G. Weiss, The complex method for interpolation of operators acting on families of Banach spaces, Lecture Notes in Math., Vol. 779, Springer-Verlag, Berlin and New York, 1980, pp. 123-153. MR 576042 (81k:46075)
- [5] T. J. Ransford, Analytic multivalued functions, Ph.D. Thesis, University of Cambridge, 1983.
- [6] Z. Slodkowski, Analytic set-valued functions and spectra, Math. Ann. 256 (1981), 363-386. MR 626955 (83b:46070)
- [7]
-, Analytic multifunctions,
-plurisubharmonic functions and uniform algebras (Proc. Conf. Banach algebras and several complex variables), F. Greenleaf and D. Gulick, editors, Contemp. Math., vol. 32, Amer. Math. Soc., Providence, R. I., 1984, pp. 243-258.
- [8] -, A generalization of Vesentini and Wermer's theorems. Rend. Sem. Mat. Univ. Padova (to appear).
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 32E20, 46E99, 46M35
Retrieve articles in all journals with MSC: 32E20, 46E99, 46M35
Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1986-0818455-X
Article copyright:
© Copyright 1986
American Mathematical Society