Characterization of nuclear Fréchet spaces in which every bounded set is polar

Seán Dineen; Reinhold Meise; Dietmar Vogt

Bulletin de la Société Mathématique de France (1984)

  • Volume: 112, page 41-68
  • ISSN: 0037-9484

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Dineen, Seán, Meise, Reinhold, and Vogt, Dietmar. "Characterization of nuclear Fréchet spaces in which every bounded set is polar." Bulletin de la Société Mathématique de France 112 (1984): 41-68. <http://eudml.org/doc/87471>.

@article{Dineen1984,
author = {Dineen, Seán, Meise, Reinhold, Vogt, Dietmar},
journal = {Bulletin de la Société Mathématique de France},
keywords = {upper semicontinuous function; plurisubharmonic; Polar sets; control sets; Fréchet spaces; Fréchet nuclear spaces with the approximation property},
language = {eng},
pages = {41-68},
publisher = {Société mathématique de France},
title = {Characterization of nuclear Fréchet spaces in which every bounded set is polar},
url = {http://eudml.org/doc/87471},
volume = {112},
year = {1984},
}

TY - JOUR
AU - Dineen, Seán
AU - Meise, Reinhold
AU - Vogt, Dietmar
TI - Characterization of nuclear Fréchet spaces in which every bounded set is polar
JO - Bulletin de la Société Mathématique de France
PY - 1984
PB - Société mathématique de France
VL - 112
SP - 41
EP - 68
LA - eng
KW - upper semicontinuous function; plurisubharmonic; Polar sets; control sets; Fréchet spaces; Fréchet nuclear spaces with the approximation property
UR - http://eudml.org/doc/87471
ER -

References

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  1. [1] BIERSTEDT (K.-D.), MEISE (R. G.) and SUMMERS (W. H.). — Köthe sets and Köthe sequence spaces, Functional Analysis, Holomorphy and Approximation Theory, J. A. BARROSO (Ed.), North Holland Mathematics Studies, Vol. 71, 1982, pp. 27-91. Zbl0504.46007MR84f:46011
  2. [2] BOLAND (P. J.) and DINEEN (S.). — Holomorphic functions on fully nuclear spaces, Bull. Soc. Math. Fr., Vol. 106, 1978, pp. 311-335. Zbl0402.46017MR81b:46060
  3. [3] BÖRGENS (M.), MEISE (R.) and VOGT (D.). — Entire functions on nuclear sequence spaces, J. reine angew. Math., Vol. 322, 1981, pp. 196-220. Zbl0441.46006MR83i:46049
  4. [4] COEURÉ (G.). — O-completion of normed linear spaces, in Proc. Coll. Anal. 1972, Herrmann, Paris, 1975, pp. 91-93. Zbl0335.46030MR53 #6273
  5. [5] DINEEN (S.). — Complex analysis in locally convex spaces, North Holland Mathematics Studies, Vol. 57, 1981. Zbl0484.46044MR84b:46050
  6. [6] DINEEN (S.), MEISE (R.) and VOGT (D.). — Caractérisation des espaces de Fréchet nucléaires dans lesquels tous les bornés sont pluripolaires, C.R. Acad. Sc. Paris, Vol. 295, 1982, pp. 385-388. Zbl0509.46001MR84b:46004
  7. [7] DINEEN (S.), MEISE (R.) and VOGT (D.). — Polar subsets of locally convex spaces, to appear in Aspects of mathematics and its applications, J. A. BARROSO (Ed.), North Holland. Zbl0602.46049
  8. [8] DINEEN (S.) and NOVERRAZ (P.). — Gaussian measures and polar sets in locally convex spaces, Ark. Mat., Vol. 17, 1979, pp. 217-223. Zbl0432.28014MR83b:32014
  9. [9] DUBINSKY (E.). — Nuclear Fréchet spaces without the bounded approximation property, Studia Math., Vol. 71, 1981, pp. 85-105. Zbl0482.46003MR83e:46007
  10. [10] DUBINSKY (E.) and VOGT (D.). — Fréchet spaces with quotients failing the bounded approximation property, preprint. Zbl0633.46003
  11. [11] GROTHENDIECK (A.). — Sur les espaces (F) et (DF), Summa Brasil Math., Vol. 3, 1954, pp. 57-122. Zbl0058.09803MR17,765b
  12. [12] LELONG (P.). — Ensembles de contrôle de croissance pour l'analyse complexe dans les espaces de Fréchet, C.R. Acad. Sc., Paris, Vol. 287, 1978, pp. 1097-1100. Zbl0403.46003MR80b:32019
  13. [13] LELONG (P.). — A class of Fréchet complex spaces in which the bounded sets are C-polar, Functional Analysis, Holomorphy and Approximation Theory, J. A. BARROSO (Ed.), North Holland Mathematics Studies, Vol. 71, 1982, pp. 255-272. Zbl0511.46046MR85d:46004
  14. [14] KISELMAN (C. O.). — Croissance des fonctions plurisousharmoniques en dimension infinie, to appear in Ann. Inst. Fourier, Vol. 34, 1984. Zbl0523.32012MR85i:32028
  15. [15] MEISE (R.) and VOGT (D.). — Structure of spaces of holomorphic functions on infinite dimensional polydiscs, Studia Math., Vol. 75, 1983, pp. 235-252. Zbl0527.46019MR85b:46052
  16. [16] MEISE (R.) and VOGT (D.). — Holomorphic functions of uniformly bounded type on nuclear Fréchet spaces, preprint. Zbl0657.46003
  17. [17] NOVERRAZ (P.). — Pseudoconvexité, convexité polynomial et domaines d'holomorphie en dimension infinie, North Holland Mathematics Studies, Vol. 3, 1973. Zbl0251.46049MR50 #10814
  18. [18] NOVERRAZ (P.). — Pseudoconvex completions of locally convex topological vector spaces, Math. Ann., Vol. 208, 1974, pp. 59-69. Zbl0264.31009MR49 #5842
  19. [19] PIETSCH (A.). — Nuclear locally convex spaces, Ergebnisse der Math., Vol. 66, Springer, 1972. Zbl0236.46001MR50 #2853
  20. [20] SCHAEFER (H. H.). — Topological vector spaces, Springer, 1971. Zbl0217.16002MR49 #7722
  21. [21] SCHOTTENLOHER (M.). — The Levi problem for domains spread over locally convex spaces with a finite dimensional Schauder decomposition, Ann. Inst. Fourier, Vol. 26, 1976, pp. 207-237. Zbl0309.32013MR58 #1262
  22. [22] SCHOTTENLOHER (M.). — Polynomial approximation on compact sets, Infinite Dimensional Holomorphy and Applications, M. C. MATOS (Ed.), North Holland Mathematics Studies, Vol. 12, 1977, pp. 379-395. Zbl0397.46044MR57 #3453
  23. [23] VOGT (D.). — Eine Charakterisierung der Potenzreihenräume von endlichem Typ und ihre Folgerungen, Manuscripta math., Vol. 37, 1982, pp. 269-301. Zbl0512.46003MR83i:46017
  24. [24] VOGT (D.). — Sequence space representations of spaces of test functions and distributions, Functional Analysis, Holomorphy and Approximation Theory, G. ZAPATA (Ed.), Marcel Dekker, Lect. Notes in Pure and Appl. Math., Vol. 83, 1983, pp. 405-443. Zbl0519.46044MR84f:46048
  25. [25] VOGT (D.). — Frécheträume, zwischen denen jede stetige lineare Abbildung beschränkt ist, J. reine angew. Math., Vol. 345, 1983, pp. 182-200. Zbl0514.46003MR85h:46007
  26. [26] VOGT (D.). — An example of a nuclear Fréchet space without the bounded approximation property, Math. Z., Vol. 182, 1983, pp. 265-267. Zbl0488.46002MR84m:46009
  27. [27] VOGT (D.) und WAGNER (M. J.). — Charakterisierung der Quotientenräume von s und eine Vermutung von Martineau, Studia Math., Vol. 67, 1980, pp. 225-240. Zbl0464.46010MR81k:46002
  28. [28] WAGNER (M. J.). — Quotientenräume von stabilen Potenzreihenräumen endlichen Typs, Manuscripta math., Vol. 31, 1980, pp. 97-109. Zbl0453.46010MR81m:46021

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