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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topDineen, 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
top- [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] 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] 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] COEURÉ (G.). — O-completion of normed linear spaces, in Proc. Coll. Anal. 1972, Herrmann, Paris, 1975, pp. 91-93. Zbl0335.46030MR53 #6273
- [5] DINEEN (S.). — Complex analysis in locally convex spaces, North Holland Mathematics Studies, Vol. 57, 1981. Zbl0484.46044MR84b:46050
- [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] 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] 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] DUBINSKY (E.). — Nuclear Fréchet spaces without the bounded approximation property, Studia Math., Vol. 71, 1981, pp. 85-105. Zbl0482.46003MR83e:46007
- [10] DUBINSKY (E.) and VOGT (D.). — Fréchet spaces with quotients failing the bounded approximation property, preprint. Zbl0633.46003
- [11] GROTHENDIECK (A.). — Sur les espaces (F) et (DF), Summa Brasil Math., Vol. 3, 1954, pp. 57-122. Zbl0058.09803MR17,765b
- [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] 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] KISELMAN (C. O.). — Croissance des fonctions plurisousharmoniques en dimension infinie, to appear in Ann. Inst. Fourier, Vol. 34, 1984. Zbl0523.32012MR85i:32028
- [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] MEISE (R.) and VOGT (D.). — Holomorphic functions of uniformly bounded type on nuclear Fréchet spaces, preprint. Zbl0657.46003
- [17] NOVERRAZ (P.). — Pseudoconvexité, convexité polynomial et domaines d'holomorphie en dimension infinie, North Holland Mathematics Studies, Vol. 3, 1973. Zbl0251.46049MR50 #10814
- [18] NOVERRAZ (P.). — Pseudoconvex completions of locally convex topological vector spaces, Math. Ann., Vol. 208, 1974, pp. 59-69. Zbl0264.31009MR49 #5842
- [19] PIETSCH (A.). — Nuclear locally convex spaces, Ergebnisse der Math., Vol. 66, Springer, 1972. Zbl0236.46001MR50 #2853
- [20] SCHAEFER (H. H.). — Topological vector spaces, Springer, 1971. Zbl0217.16002MR49 #7722
- [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] 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] VOGT (D.). — Eine Charakterisierung der Potenzreihenräume von endlichem Typ und ihre Folgerungen, Manuscripta math., Vol. 37, 1982, pp. 269-301. Zbl0512.46003MR83i:46017
- [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] 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] 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] 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] WAGNER (M. J.). — Quotientenräume von stabilen Potenzreihenräumen endlichen Typs, Manuscripta math., Vol. 31, 1980, pp. 97-109. Zbl0453.46010MR81m:46021
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