Some characterizations of ultrabornological spaces

Valdivia, Manuel. "Some characterizations of ultrabornological spaces." Annales de l'institut Fourier 24.3 (1974): 57-66. <http://eudml.org/doc/74192>.

@article{Valdivia1974,
abstract = {Let $U$ be an infinite-dimensional separable Fréchet space with a topology defined by a family of norms. Let $F$ be an infinite-dimensional Banach space. Then $F$ is the inductive limit of a family of spaces equal to $E$. The choice of suitable classes of Fréchet spaces allows to give characterizations of ultrabornological spaces using the result above.. Let $\Omega $ be a non-empty open set in the euclidean $n$-dimensional space $R^n$. Then $F$ is the inductive limit of a family of spaces equal to $\{\bf D\}(\Omega )$.},
author = {Valdivia, Manuel},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {3},
pages = {57-66},
publisher = {Association des Annales de l'Institut Fourier},
title = {Some characterizations of ultrabornological spaces},
url = {http://eudml.org/doc/74192},
volume = {24},
year = {1974},
}

TY - JOUR
AU - Valdivia, Manuel
TI - Some characterizations of ultrabornological spaces
JO - Annales de l'institut Fourier
PY - 1974
PB - Association des Annales de l'Institut Fourier
VL - 24
IS - 3
SP - 57
EP - 66
AB - Let $U$ be an infinite-dimensional separable Fréchet space with a topology defined by a family of norms. Let $F$ be an infinite-dimensional Banach space. Then $F$ is the inductive limit of a family of spaces equal to $E$. The choice of suitable classes of Fréchet spaces allows to give characterizations of ultrabornological spaces using the result above.. Let $\Omega $ be a non-empty open set in the euclidean $n$-dimensional space $R^n$. Then $F$ is the inductive limit of a family of spaces equal to ${\bf D}(\Omega )$.
LA - eng
UR - http://eudml.org/doc/74192
ER -