@article{BSMF_1984__112__41_0, author = {Dineen, Se\'an and Meise, Reinhold and Vogt, Dietmar}, title = {Characterization of nuclear Fr\'echet spaces in which every bounded set is polar}, journal = {Bulletin de la Soci\'et\'e Math\'ematique de France}, volume = {112}, year = {1984}, pages = {41-68}, doi = {10.24033/bsmf.2000}, mrnumber = {86e:46002}, zbl = {0556.46003}, language = {en}, url = {http://dml.mathdoc.fr/item/BSMF_1984__112__41_0} }
Dineen, Seán; Meise, Reinhold; Vogt, Dietmar. Characterization of nuclear Fréchet spaces in which every bounded set is polar. Bulletin de la Société Mathématique de France, Tome 112 (1984) pp. 41-68. doi : 10.24033/bsmf.2000. http://gdmltest.u-ga.fr/item/BSMF_1984__112__41_0/
[1] 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. | MR 84f:46011 | Zbl 0504.46007
, and . -[2] Holomorphic functions on fully nuclear spaces, Bull. Soc. Math. Fr., Vol. 106, 1978, pp. 311-335. | Numdam | MR 81b:46060 | Zbl 0402.46017
and . -[3] Entire functions on nuclear sequence spaces, J. reine angew. Math., Vol. 322, 1981, pp. 196-220. | MR 83i:46049 | Zbl 0441.46006
, and . -[4] O-completion of normed linear spaces, in Proc. Coll. Anal. 1972, Herrmann, Paris, 1975, pp. 91-93. | MR 53 #6273 | Zbl 0335.46030
. -[5] Complex analysis in locally convex spaces, North Holland Mathematics Studies, Vol. 57, 1981. | MR 84b:46050 | Zbl 0484.46044
. -[6] Caractérisation des espaces de Fréchet nucléaires dans lesquels tous les bornés sont pluripolaires, C.R. Acad. Sc. Paris, Vol. 295, 1982, pp. 385-388. | MR 84b:46004 | Zbl 0509.46001
, and . -[7] Polar subsets of locally convex spaces, to appear in Aspects of mathematics and its applications, J. A. BARROSO (Ed.), North Holland. | Zbl 0602.46049
, and . -[8] Gaussian measures and polar sets in locally convex spaces, Ark. Mat., Vol. 17, 1979, pp. 217-223. | MR 83b:32014 | Zbl 0432.28014
and . -[9] Nuclear Fréchet spaces without the bounded approximation property, Studia Math., Vol. 71, 1981, pp. 85-105. | MR 83e:46007 | Zbl 0482.46003
. -[10] Fréchet spaces with quotients failing the bounded approximation property, preprint.
and . -[11] Sur les espaces (F) et (DF), Summa Brasil Math., Vol. 3, 1954, pp. 57-122. | MR 17,765b | Zbl 0058.09803
. -[12] 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. | MR 80b:32019 | Zbl 0403.46003
. -[13] 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. | MR 85d:46004 | Zbl 0511.46046
. -[14] Croissance des fonctions plurisousharmoniques en dimension infinie, to appear in Ann. Inst. Fourier, Vol. 34, 1984. | Numdam | MR 85i:32028 | Zbl 0523.32012
. -[15] Structure of spaces of holomorphic functions on infinite dimensional polydiscs, Studia Math., Vol. 75, 1983, pp. 235-252. | MR 85b:46052 | Zbl 0527.46019
and . -[16] Holomorphic functions of uniformly bounded type on nuclear Fréchet spaces, preprint.
and . -[17] Pseudoconvexité, convexité polynomial et domaines d'holomorphie en dimension infinie, North Holland Mathematics Studies, Vol. 3, 1973. | MR 50 #10814 | Zbl 0251.46049
. -[18] Pseudoconvex completions of locally convex topological vector spaces, Math. Ann., Vol. 208, 1974, pp. 59-69. | MR 49 #5842 | Zbl 0264.31009
. -[19] Nuclear locally convex spaces, Ergebnisse der Math., Vol. 66, Springer, 1972. | MR 50 #2853 | Zbl 0236.46001
. -[20] Topological vector spaces, Springer, 1971. | MR 49 #7722 | Zbl 0217.16002
. -[21] 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. | Numdam | MR 58 #1262 | Zbl 0309.32013
. -[22] Polynomial approximation on compact sets, Infinite Dimensional Holomorphy and Applications, M. C. MATOS (Ed.), North Holland Mathematics Studies, Vol. 12, 1977, pp. 379-395. | MR 57 #3453 | Zbl 0397.46044
. -[23] Eine Charakterisierung der Potenzreihenräume von endlichem Typ und ihre Folgerungen, Manuscripta math., Vol. 37, 1982, pp. 269-301. | MR 83i:46017 | Zbl 0512.46003
. -[24] 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. | MR 84f:46048 | Zbl 0519.46044
. -[25] Frécheträume, zwischen denen jede stetige lineare Abbildung beschränkt ist, J. reine angew. Math., Vol. 345, 1983, pp. 182-200. | MR 85h:46007 | Zbl 0514.46003
. -[26] An example of a nuclear Fréchet space without the bounded approximation property, Math. Z., Vol. 182, 1983, pp. 265-267. | MR 84m:46009 | Zbl 0488.46002
. -[27] Charakterisierung der Quotientenräume von s und eine Vermutung von Martineau, Studia Math., Vol. 67, 1980, pp. 225-240. | MR 81k:46002 | Zbl 0464.46010
und . -[28] Quotientenräume von stabilen Potenzreihenräumen endlichen Typs, Manuscripta math., Vol. 31, 1980, pp. 97-109. | MR 81m:46021 | Zbl 0453.46010
. -