A class of locally convex spaces without 𝒞 -webs

Manuel Valdivia

Annales de l'institut Fourier (1982)

  • Volume: 32, Issue: 2, page 261-269
  • ISSN: 0373-0956

Abstract

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In this article we give some properties of the tensor product, with the ϵ and π topologies, of two locally convex spaces. As a consequence we prove that the theory of M. de Wilde of the closed graph theorem does not contain the closed graph theorem of L. Schwartz.

How to cite

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Valdivia, Manuel. "A class of locally convex spaces without ${\mathcal {C}}$-webs." Annales de l'institut Fourier 32.2 (1982): 261-269. <http://eudml.org/doc/74540>.

@article{Valdivia1982,
abstract = {In this article we give some properties of the tensor product, with the $\varepsilon $ and $\pi $ topologies, of two locally convex spaces. As a consequence we prove that the theory of M. de Wilde of the closed graph theorem does not contain the closed graph theorem of L. Schwartz.},
author = {Valdivia, Manuel},
journal = {Annales de l'institut Fourier},
keywords = {tensor product; Suslin space; De Wilde's closed graph theorem; Schwartz' closed graph theorem},
language = {eng},
number = {2},
pages = {261-269},
publisher = {Association des Annales de l'Institut Fourier},
title = {A class of locally convex spaces without $\{\mathcal \{C\}\}$-webs},
url = {http://eudml.org/doc/74540},
volume = {32},
year = {1982},
}

TY - JOUR
AU - Valdivia, Manuel
TI - A class of locally convex spaces without ${\mathcal {C}}$-webs
JO - Annales de l'institut Fourier
PY - 1982
PB - Association des Annales de l'Institut Fourier
VL - 32
IS - 2
SP - 261
EP - 269
AB - In this article we give some properties of the tensor product, with the $\varepsilon $ and $\pi $ topologies, of two locally convex spaces. As a consequence we prove that the theory of M. de Wilde of the closed graph theorem does not contain the closed graph theorem of L. Schwartz.
LA - eng
KW - tensor product; Suslin space; De Wilde's closed graph theorem; Schwartz' closed graph theorem
UR - http://eudml.org/doc/74540
ER -

References

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  1. [1] I. AMEMIYA and Y. KOMURA, Über nich-vollständinge Montelräume, Math. Ann., 177 (1968), 273-277. Zbl0157.43903MR38 #508
  2. [2] N. BOURBAKI, Éléments de Mathématique, Topologie Générale Chap. IX, Hermann, Paris, 1974. 
  3. [3] N. BOURBAKI, Éléments de Mathématique, Espaces vectoriels topologiques, Act. Sci. et Ind., Paris, vol. 1929 (1955). 
  4. [4] M. DE WILDE, Réseaux dans les espaces linéaires à semi-normes, Mém. Soc. Royale Sci. Liège, 18 (5), 2 (1969), 1-144. Zbl0199.18103MR44 #3102
  5. [5] G. KÖTHE, Topological Vector Spaces II, Springer-Verlag, New York-Heidelberg-Berlin, 1979. Zbl0417.46001
  6. [6] H. LÖWIG, Über Die dimension linearer Räume, Studia Math., (1934), 18-23. Zbl0010.30404JFM60.1229.01
  7. [7] A. MARTINEAU, Sur le théorème du graphe fermé, C.R. Acad. Sci., Paris, 263 (1966), 870-871. Zbl0151.19203MR34 #6495
  8. [8] L. SCHWARTZ, Sur le théorème de graphe fermé. C.R. Acad. Sci., Paris 263 (1966), 602-605. Zbl0151.19202MR34 #6494
  9. [9] M. VALDIVIA, Absolutely convex sets in barrelled spaces, Ann. Inst. Fourier, Grenoble, 21, 2 (1971), 3-13. Zbl0205.40904MR48 #11968
  10. [10] M. VALDIVIA, On suprabarrelled spaces. Functional Analysis, Holomorphy and Approximation Theory. Proocedings, Rio de Janeiro 1978, Lecture Notes in Math., 843 (1981), 572-580, Springer-Verlag, New York-Heidelberg-Berlin. Zbl0469.46001MR82h:46003

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