Holomorphic functions on strict inductive limits of Banach spaces.

Seán Dineen; Luiza A. Moraes

Revista Matemática de la Universidad Complutense de Madrid (1992)

  • Volume: 5, Issue: 2-3, page 177-183
  • ISSN: 1139-1138

Abstract

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In this article we show that a number of apparently different properties coincide on the set of holomorphic functions on a strict inductive limit (all inductive limits are assumed to be countable and proper) of Banach spaces and that they are all satisfied only in the trivial case of a strict inductive limit of finite dimensional spaces. Thus the linear properties of a strict inductive limit of Banach spaces rarely translate themselves into holomorphic properties.

How to cite

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Dineen, Seán, and Moraes, Luiza A.. "Holomorphic functions on strict inductive limits of Banach spaces.." Revista Matemática de la Universidad Complutense de Madrid 5.2-3 (1992): 177-183. <http://eudml.org/doc/44317>.

@article{Dineen1992,
abstract = {In this article we show that a number of apparently different properties coincide on the set of holomorphic functions on a strict inductive limit (all inductive limits are assumed to be countable and proper) of Banach spaces and that they are all satisfied only in the trivial case of a strict inductive limit of finite dimensional spaces. Thus the linear properties of a strict inductive limit of Banach spaces rarely translate themselves into holomorphic properties.},
author = {Dineen, Seán, Moraes, Luiza A.},
journal = {Revista Matemática de la Universidad Complutense de Madrid},
keywords = {Funciones holomorfas; Límite inductivo; Espacios de Banach; Espacios localmente convexos; set of holomorphic functions on a strict inductive limit},
language = {eng},
number = {2-3},
pages = {177-183},
title = {Holomorphic functions on strict inductive limits of Banach spaces.},
url = {http://eudml.org/doc/44317},
volume = {5},
year = {1992},
}

TY - JOUR
AU - Dineen, Seán
AU - Moraes, Luiza A.
TI - Holomorphic functions on strict inductive limits of Banach spaces.
JO - Revista Matemática de la Universidad Complutense de Madrid
PY - 1992
VL - 5
IS - 2-3
SP - 177
EP - 183
AB - In this article we show that a number of apparently different properties coincide on the set of holomorphic functions on a strict inductive limit (all inductive limits are assumed to be countable and proper) of Banach spaces and that they are all satisfied only in the trivial case of a strict inductive limit of finite dimensional spaces. Thus the linear properties of a strict inductive limit of Banach spaces rarely translate themselves into holomorphic properties.
LA - eng
KW - Funciones holomorfas; Límite inductivo; Espacios de Banach; Espacios localmente convexos; set of holomorphic functions on a strict inductive limit
UR - http://eudml.org/doc/44317
ER -

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