Metrizability of spaces of holomorphic functions

López-Salazar Codes, Jerónimo (2009). Metrizability of spaces of holomorphic functions. "Journal of Mathematical Analysis And Applications", v. 355 (n. 1); pp. 434-438. ISSN 0022-247X. https://doi.org/10.1016/j.jmaa.2009.01.063.

Description

Title: Metrizability of spaces of holomorphic functions
Author/s:
  • López-Salazar Codes, Jerónimo
Item Type: Article
Título de Revista/Publicación: Journal of Mathematical Analysis And Applications
Date: 2009
ISSN: 0022-247X
Volume: 355
Subjects:
Freetext Keywords: Holomorphic function, Nachbin–Coeuré topology, Bounding set, Limited set
Faculty: E.U.I.T. Telecomunicación (UPM)
Department: Matemática Aplicada a la Ingeniería Técnica de Telecomunicación [hasta 2014]
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

In this paper we prove that if U is an open subset of a metrizable locally convex space E of infinite dimension, the space H(U) of all holomorphic functions on U, endowed with the Nachbin–Coeuré topology τδ, is not metrizable. Our result can be applied to get that, for all usual topologies, H(U) is metrizable if and only if E has finite dimension. RESUMEN. En este artículo se demuestra que si U es un abierto en un espacio E localmente convexo metrizable de dimensión infinita y H(U) es el espacio de funciones holomorfas en U, entonces la topología de Nachbin-Coeuré en H(U) no es metrizable. Este resultado se utiliza para demostrar que las topologías habituales en H(U) son metrizables si y sólo si E tiene dimensión finita.

More information

Item ID: 22361
DC Identifier: http://oa.upm.es/22361/
OAI Identifier: oai:oa.upm.es:22361
DOI: 10.1016/j.jmaa.2009.01.063
Official URL: http://www.sciencedirect.com/science/article/pii/S0022247X09001103
Deposited by: Memoria Investigacion
Deposited on: 05 Mar 2014 14:38
Last Modified: 21 Apr 2016 14:15
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