Some characterizations of ultrabornological spaces
Annales de l'Institut Fourier, Tome 24 (1974) no. 3, pp. 57-66.

Dans cet article on démontre que E étant un espace de Fréchet séparable de dimension infinie dont la topologie est définie par une famille de normes, et F étant un espace de Banach de dimension infinie, F est la limite inductive d’une famille d’espaces égaux à E. Le choix de classes convenables d’espaces de Fréchet permet de trouver des caractéristiques d’espaces ultra-bornologiques, en utilisant le résultat antérieur. On démontre aussi que Ω est un ouvert non-vide de l’espace euclidien Rn, F est la limite inductive d’une famille d’espaces égaux à D(Ω).

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 Ω be a non-empty open set in the euclidean n-dimensional space Rn. Then F is the inductive limit of a family of spaces equal to D(Ω).

@article{AIF_1974__24_3_57_0,
     author = {Valdivia, Manuel},
     title = {Some characterizations of ultrabornological spaces},
     journal = {Annales de l'Institut Fourier},
     pages = {57--66},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {24},
     number = {3},
     year = {1974},
     doi = {10.5802/aif.519},
     mrnumber = {51 #6344},
     zbl = {0287.46001},
     language = {en},
     url = {https://www.numdam.org/articles/10.5802/aif.519/}
}
TY  - JOUR
AU  - Valdivia, Manuel
TI  - Some characterizations of ultrabornological spaces
JO  - Annales de l'Institut Fourier
PY  - 1974
SP  - 57
EP  - 66
VL  - 24
IS  - 3
PB  - Institut Fourier
PP  - Grenoble
UR  - https://www.numdam.org/articles/10.5802/aif.519/
DO  - 10.5802/aif.519
LA  - en
ID  - AIF_1974__24_3_57_0
ER  - 
%0 Journal Article
%A Valdivia, Manuel
%T Some characterizations of ultrabornological spaces
%J Annales de l'Institut Fourier
%D 1974
%P 57-66
%V 24
%N 3
%I Institut Fourier
%C Grenoble
%U https://www.numdam.org/articles/10.5802/aif.519/
%R 10.5802/aif.519
%G en
%F AIF_1974__24_3_57_0
Valdivia, Manuel. Some characterizations of ultrabornological spaces. Annales de l'Institut Fourier, Tome 24 (1974) no. 3, pp. 57-66. doi : 10.5802/aif.519. https://www.numdam.org/articles/10.5802/aif.519/

[1] A.I. Markushevich, Sur les bases (au sens large) dans les espaces linéaires, Doklady Akad. Nauk SSSR (N.S.), 41, (1934) 227-229. | Zbl

[2] J.T. Marti, Introduction to the Theory of Bases, Springer-Verlag, Berlin-Heidelberg-New York, 1969. | MR | Zbl

[3] A. Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc., No. 16 (1966). | Zbl

[4] M. Valdivia, A class of precompact sets in Banach spaces., J. reine angew. Math. (To appear). | Zbl

  • Dabrowski, Yoann; Brouder, Christian Functional Properties of Hörmander’s Space of Distributions Having a Specified Wavefront Set, Communications in Mathematical Physics, Volume 332 (2014) no. 3, p. 1345 | DOI:10.1007/s00220-014-2156-0
  • References, Barrelled Locally Convex Spaces, Volume 131 (1987), p. 484 | DOI:10.1016/s0304-0208(08)71679-7
  • Jarchow, Hans On Certain Locally Convex Topologies on Banach Spaces, Functional Analysis: Surveys and Recent Results III, Proceedings of the Conference on Functional Analysis, Volume 90 (1984), p. 79 | DOI:10.1016/s0304-0208(08)71468-3
  • Bibliography, Nuclear and Conuclear Spaces, Volume 52 (1981), p. 263 | DOI:10.1016/s0304-0208(08)71561-5
  • Floret, Klaus Some Aspects of the Theory of Locally Convex Inductive Limits, Functional Analysis: Surveys and Recent Results II, Volume 38 (1980), p. 205 | DOI:10.1016/s0304-0208(08)70809-0
  • Valdivia, Manuel Quotients of complete locally convex spaces, Manuscripta Mathematica, Volume 14 (1974) no. 3, p. 235 | DOI:10.1007/bf01171409

Cité par 6 documents. Sources : Crossref