Representation of Spaces of Entire Functions on Banach Spaces
José M. Ansemil, Richard M. Aron, and Socorro Ponte
Source: Publ. Res. Inst. Math. Sci. Volume 45, Number 2 (2009), 383-391.
Abstract
We prove the impossibility of expressing the space of entire functions on any infinite dimensional complex Banach space with a Schauder basis $E$ as a countable union of spaces of entire functions that are bounded on countable open covers of $E$.
Primary Subjects: 46G20
Secondary Subjects: 46A03, 46A13
Keywords: Entire function on a Banach space; inductive limit; Schauder basis
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.prims/1241553124
Digital Object Identifier: doi:10.2977/prims/1241553124
Zentralblatt MATH identifier:
05591477
References
R. M. Aron, Entire functions of unbounded type on a Banach space, Boll. Un. Mat. Ital. (4) 9 (1974), 28--31.
Mathematical Reviews (MathSciNet):
MR374911
G. Coeuré, Fonctions plurisousharmoniques sur les espaces vectoriels topologiques et applications àe l'étude des fonctions analytiques, Ann. Inst. Fourier (Grenoble) 20 (1970), fasc. 1, 361--432.
Mathematical Reviews (MathSciNet):
MR274804
S. Dineen, Complex analysis on infinite-dimensional spaces, Springer Monographs in Mathematics, Springer, London, 1999.
Mathematical Reviews (MathSciNet):
MR1705327
J. Lindenstrauss and L. Tzafriri, Classical Banach spaces. I and II, Classics in Mathematics, Springer, Berlin, 1977.
Mathematical Reviews (MathSciNet):
MR500056
J. Mujica, Spaces of germs of holomorphic functions, in Studies in analysis, Adv. in Math. Suppl. Stud. 4, 1--41, Academic Press, New York, 1979.
Mathematical Reviews (MathSciNet):
MR546801
L. Nachbin, Topology on spaces of holomorphic mappings, Ergebnisse der Mathematik und ihrer Grenzgebiete 47, Springer-Verlag New York Inc., New York, 1969.
Mathematical Reviews (MathSciNet):
MR254579
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