Vector spaces of entire functions of unbounded type

López-Salazar Codes, Jerónimo (2011). Vector spaces of entire functions of unbounded type. "Proceedings of the American Mathematical Society", v. 139 (n. 4); pp. 1347-1360. ISSN 0002-9939.

Description

Title: Vector spaces of entire functions of unbounded type
Author/s:
  • López-Salazar Codes, Jerónimo
Item Type: Article
Título de Revista/Publicación: Proceedings of the American Mathematical Society
Date: April 2011
ISSN: 0002-9939
Volume: 139
Subjects:
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

Let E be an infinite dimensional complex Banach space. We prove the existence of an infinitely generated algebra, an infinite dimensional closed subspace and a dense subspace of entire functions on E whose non-zero elements are functions of unbounded type. We also show that the τδ topology on the space of all holomorphic functions cannot be obtained as a countable inductive limit of Fr´echet spaces. RESUMEN. Sea E un espacio de Banach complejo de dimensión infinita y sea H(E) el espacio de funciones holomorfas definidas en E. En el artículo se demuestra la existencia de un álgebra infinitamente generada en H(E), un subespacio vectorial en H(E) cerrado de dimensión infinita y un subespacio denso en H(E) cuyos elementos no nulos son funciones de tipo no acotado. También se demuestra que el espacio de funciones holomorfas con la topología ? no es un límite inductivo numberable de espacios de Fréchet.

More information

Item ID: 22362
DC Identifier: http://oa.upm.es/22362/
OAI Identifier: oai:oa.upm.es:22362
Official URL: http://www.ams.org/proc/2011-139-04/S0002-9939-2010-10817-1/S0002-9939-2010-10817-1.pdf
Deposited by: Memoria Investigacion
Deposited on: 10 Mar 2014 15:45
Last Modified: 21 Apr 2016 14:15
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