Previous |  Up |  Next

Article

Title: Some aspects of the theory of barreled spaces (English)
Title: Některé otázky teorie sudovitých prostorů (Czech)
Author: Pérez Carreras, Pedro
Language: English
Journal: Časopis pro pěstování matematiky
ISSN: 0528-2195
Volume: 112
Issue: 2
Year: 1987
Pages: 123-161
Summary lang: English
Summary lang: Czech
Summary lang: Russian
.
Category: math
.
MSC: 46A08
idZBL: Zbl 0656.46001
idMR: MR897640
DOI: 10.21136/CPM.1987.118303
.
Date available: 2009-09-23T09:40:55Z
Last updated: 2020-07-29
Stable URL: http://hdl.handle.net/10338.dmlcz/118303
.
Reference: [1] N. Adasch B. Ernst D. Keim: Topological Vector Spaces.Springer, 1978. MR 0487376
Reference: [2] I. Amemiya Y. Komura: Über nicht-vollständige Montelräume.Math. Ann. 177 (1968), 273-277. MR 0232182
Reference: [3] D. Amir J. Lindenstrauss: The structure of weakly compact sets in Banach space.
Reference: [4] J. Arias: Dense hyperplanes of first category.Math. Ann., 249 (1980), 111-114. Zbl 0419.46015, MR 0578718
Reference: [5] J. Arias: Normed barely Baire spaces.Israel J. Math., 42 (1982), 33 - 36. Zbl 0495.46004, MR 0687932
Reference: [6] J. Arias: $l_0^\infty(\Sigma)$ no es totalmente tonelado.Rev. Real Acad. Ci. Madrid (to be published).
Reference: [7] J. Bait P. Dierolf J. Voigt: Summable sequences and topological properties of $m(l)$.Arch. d. Math.
Reference: [8] Y. Benyamini M. E. Rudin M. Wage: Continuous images of weakly compact subsets of Banach spaces.Pacific J. Math. (1977). MR 0625889
Reference: [9] J. Bonet P. Perez Carreras: Some results on barreledness in projective tensor products.Math. Z., 185 (1984), 333-338. MR 0731681
Reference: [10] J. Bonet P. Pérez Carreras: On the three-space-problem for certain classes of Baire-like spaces.Bull. Soc. Roy. Sci. Liege, 51 année, 9-12 (1982), 381 - 385. MR 0705014
Reference: [11] J. Bonet P. Pérez Carreras: Remarks on the stability of barreled-type topologies.Bull. Soc. Roy. Sci. Liege, 52 (1983), 313-318. MR 0731286
Reference: [12] M. De Wilde: Vector topologies and linear maps on products of topological vector spaces.Math. Ann., 196 (1972), 117-128. MR 0298374
Reference: [13] M. De Wilde: Closed graph theorems and webbed spaces.Pitman, 1978. Zbl 0373.46007
Reference: [14] M. De Wilde J. Schmets: Locally convex topologies strictly finer than a given topology and preserving barrelledness or similar properties.Bull. Soc. Roy. Sci. Liège, 41 (1972), 268-271. MR 0312187
Reference: [15] S. Dierolf: A note on the lifting of linear and locally convex topologies on a quotient space.Collect. Math., 31 (1980), 60-62. Zbl 0453.46002, MR 0621724
Reference: [16] J. Dieudonné: Sur les propriétés de permanence de certain espaces vectoriels topolgiques.Ann. Soc. Polon. Math., 25 (1952), 50-55 (1953). MR 0056189
Reference: [17] L. Drewnowski: Un theoreme sur les operateurs de $l^\infty(\Gamma)$.C.R. Acad. Sci. Paris t. 281, serie A-967. MR 0385626
Reference: [18] P. Dierolf S. Dierolf L. Drewnowski: Remarks and examples concerning unordered-Baire-like spaces and ultrabarrelled spaces.Coll. Math. 39 110-117.
Reference: [19] N. Dunford J. Schwartz: Linear Operators Vol. 1.Interscience 1958.
Reference: [20] V. Eberhardt: Über Komuras Graphenstaz: Vollständigkeit, Permanenzeigenschaften und Beispiele.Habilitationsschrift, München 1977.
Reference: [21] M. Eidelheit: Zur Theorie der Systeme linearer Gleichungen.Studia Math., 6 (1936), 139-148. Zbl 0015.35603
Reference: [22] K. Floret: Folgenretraktive Sequenzen lokalkonvexer Räume.J. Reine u. Angew. Math., 259 (1973), 65-85. Zbl 0251.46003, MR 0313748
Reference: [23] Grothendieck A.: Produits tensoriels topologiques.Mem. A.M.S. 16 1955. Zbl 0123.30301, MR 0075539
Reference: [24] A. Grotendieck: Sur les espaces (F) et (DF).Summa Brasil. Math. 3, (1954), 57-121. MR 0075542
Reference: [25] C. Harvey, F. R.: Open mappings and the lack of fully completeness of $D'(\Omega)$.Proc. A.M.S. 25 (1970), 786-790. Zbl 0197.39101, MR 0265906
Reference: [26] R. Hollstein: Über die Tonneliertheit von lokalkonvexen Tensorprodukten.Manusc. Math., 22 (1977), 7-12. Zbl 0359.46046, MR 0482032
Reference: [27] J. Horvath: Topological Vector Spaces and Distributions, Vol I.Addison-Wesley 1966. Zbl 0143.15101, MR 0205028
Reference: [28] H. Jarchow: Locally Convex Spaces.Teubner 1981. Zbl 0466.46001, MR 0632257
Reference: [29] J. Izquierdo: Sobre ciertas clases de espacios hipertonelados.Tesis Doctoral, Valencia 1982.
Reference: [30] N. Kalton: Some forms of the closed graph theorem.Proc. Cambridge Phil. Soc., 70 (1971), 401-408. Zbl 0221.46006, MR 0301476
Reference: [31] J. L. Kelley I. Namioka: Linear Topological Spaces.van Nostrand 1963. MR 0166578
Reference: [32] Y. Komura: On linear topological spaces.Kumamoto J. Sci. Ser. A 5 (1962), 148-157. Zbl 0105.30803, MR 0151817
Reference: [33] G. Köthe: Topologische Lineare Raume I.Springer 1966. MR 0194863
Reference: [34] G. Köthe: Topological Vector Spaces II.Springer 1979. MR 0551623
Reference: [35] M. Mahowald: Barrelled spaces and the closed graph theorem.J. London Math. Soc, 36 (1961), 108- 110. Zbl 0097.09001, MR 0125426
Reference: [36] B. M. Makarov: On some pathological properties of inductive limits of Banach spaces.(russian). Uspehi Math. Nauk, 18, Nr. 111, (1963), 171-178. MR 0152867
Reference: [37] A. Marquina: A note on the closed graph theorem.Arch. der Math. 28 (1977), 82-85. Zbl 0351.46003, MR 0430726
Reference: [38] A. Marquina J. M. Sanz Serna: Barrelledness conditions on $c_0(E)$.Arch. der Math., 31 (1978), 589-596. MR 0531574
Reference: [39] J. M. Mazón: Some classes of locally convex spaces.Arch. der Math. 38 (1982), 131-137. MR 0650344
Reference: [40] E. Michael M. E. Rudin: A note on Eberlein compacts.Pacific J. Math., 72 (1977), 487-495. MR 0478092
Reference: [41] A. Moltó: On uniform boundedness properties in exhausting additive set function spaces.Proc Roy. Soc. Edinburgh, 90 A (1981), 175-184. MR 0636071
Reference: [42] J. Motos: Resultados en dos nuevas clases de espacios localmente convexos.Tesis Doctoral, Valencia 1974.
Reference: [43] V. Moscatelli: Sur une classe d'espaces localment convexes B-complets.C.R. Acad. Sci., Paris, A. 276 (1973), 1205-1208. MR 0324362
Reference: [44] M. Oberguggenberger: Der Grapehnsatz in lokalkonvexen topologischen Vektorräumen.Teubner-Texte Band 44, 1982. MR 0685147
Reference: [45] P. Pérez Carreras: Una nota sobre espacios DF.Rev Real Acad. Ci. Madrid, 75 (1981), 739-741. MR 0650044
Reference: [46] P. Pérez Carreras: Sobre ciertas clases de espacios vectoriales topologicos.Rev. Real Acad. Ci. Madrid, 76 (1982), 585-594.
Reference: [47] P. Pérez Carreras J. Bonet: Remarks and examples concerning suprabarreled and totally barreled spaces.Arch, der Math., 39 (1982), 340-347. MR 0684404
Reference: [48] P. Pérez Carreras J. Bonet: Espacios Tonelados.Public. Univ. Sevilla 1980.
Reference: [49] A. Pietsch: Nuclear Locally convex Spaces.Springer 1972. Zbl 0308.47024, MR 0350360
Reference: [50] J. O. Popoola I. Tweddle: Density character, barrelledness and the closed graph theorem.Coll, Math., 40 (1979), 249-258. MR 0547867
Reference: [51] V. Pták: On complete topological linear spaces.(russian). Cehosl. Mat. Z., 78, 3 (1953), 301-364; english: A.M.S. Transl. (2), 110 (1977), 61-106. MR 0064303
Reference: [52] V. Pták: Completeness and the open mapping theorem.Bull. Soc Math. France, 86 (1958), 41-74. MR 0105606
Reference: [53] D. A. Raikov: Closed graph theorems and the completeness of topological linear spaces.(russian) Proc. Fourth All-Union Math. Congr. (Leningrad, 1961) Vol. II, 317-323. Izdat. "Nauka", Leningrad 1964. MR 0220038
Reference: [54] D. A. Raikov: Double closed-graph theorem for topological linear spaces.Siber. math. J., 7 (1966), 287-300. Zbl 0171.10701, MR 0198196
Reference: [55] W. Roelcke S. Dierolf: On the three-space-problem for topological vector spaces.Collect. Math., 32(1981), 13-35. MR 0643398
Reference: [56] H. P. Rosenthal: On relatively disjoint families of measures with some applications to Banach space theory.Studia Math., 37 (1970), 13 - 36. Zbl 0227.46027, MR 0270122
Reference: [57] H. Saiflu I. Tweddle: From B-completeness to countable codimensional subspaces via the closed graph theorem.Proc. Roy. Soc. Edinburgh 86 A 107-114, (1980). MR 0580250
Reference: [58] H. Saiflu I. Tweddle: The domain spaces for Marquina's closed graph theorem.Archiv der Math., 34 (1980), 463-468. MR 0593773
Reference: [59] S. Saxon: Some normed barreled spaces which are not Baire.Math. Ann., 209 (1974), 153-160. MR 0352925
Reference: [60] S. Saxon: Two characterizations of linear Baire spaces.Proc. A.M.S., 45, (1974). Zbl 0294.46003, MR 0358274
Reference: [61] S. Saxon: Nuclear and product spaces, Baire-like spaces and the strongest locally convex topology.Math. Ann., 197 (1972), 87-106. MR 0305010
Reference: [62] S. Saxon M. Levin: Every countable-codimensional subspace of a barrelled space is barrelled.Proc. A.M.S., 29 (1971), 91-96. MR 0280972
Reference: [63] S. Saxon P. Narayanaswami: Metrizable (LF)-spaces, (db)-spaces and the separable quotient problem.Bull. Austral. Math. Soc., 23 (1981), 65-80. MR 0615133
Reference: [64] S. Saxon A. Wilansky: The equivalence of some Banach space problems.Coll. Math., 37 (1977), 217-226. MR 0511780
Reference: [65] W. Slowikowski: Quotient spaces and the open map theorem.Bull. A.M.S., 67 (1961), 498-500. Zbl 0100.32601, MR 0131743
Reference: [66] J. Schmets: Espaces de fonctions continues.Lect. Notes in Math. 519, Springer 1976. Zbl 0334.46022, MR 0423058
Reference: [67] E. T. Shavgulidze: On the hypercompleteness of locally convex spaces.Math. Notes 13 (1973), 180-182. MR 0344839
Reference: [68] E. T. Shavgulidze: Br-completeness.Funct. Anal. Appl. 9 (1975), 363-364.
Reference: [69] O. K. Smoljanov: The space D is not hereditarily complete.Math. USSR, Izvestija 5 (1971), 696-710.
Reference: [70] A. Todd S. Saxon: A property of locally convex Baire spaces.Math. Ann., 206 (1973), 23-32. MR 0328523
Reference: [71] I. Tweddle F. E. Yeomans: On the stability of barrelled topologies II.Glasgow Math. J., 21 (1980), 91-95. MR 0558281
Reference: [72] M. Valdivia: On certain normed barrelled spaces.Ann. Inst. Fourier, 29 (1979), 39-56. MR 0552959
Reference: [73] M. Valdivia: Topics in Locally Convex Spaces.North Holland 1982. Zbl 0489.46001, MR 0671092
Reference: [74] M. Valdivia: Absolutely convex sets in barrlled spaces.Ann. Inst. Fourier, 21 (1971), 3-13. MR 0333643
Reference: [75] M. Valdivia: On suprabarreled spaces.Proc. Funct. Anal., holomorphy and approx. theory (Rio de Janeiro 1978) Lect. Notes in Math. 843 Springer 1981. MR 0610847
Reference: [76] M. Valdivia: The space of distributions $D'(\Omega)$ is not $B_r$-complete.Math. Ann., 211 (1974), 145-149. Zbl 0288.46033, MR 0370177
Reference: [77] M. Valdivia: On $B_r$-completeness.Ann. Inst. Fourier, 25 (1975), 29-43. Zbl 0301.46004, MR 0399792
Reference: [78] M. Valdivia: The space $D(\Omega$)$ is not $B_r$-complete.Ann. Inst. Fourier 27 (1977), 29-43. MR 0477665
Reference: [79] M. Valdivia: Some examples on quasi-barrelled spaces.Ann. Inst. Fourier, 22 (1972), 21-26. Zbl 0226.46005, MR 0336277
Reference: [80] M. Valdivia: Mackey convergence and the closed graph theorem.Arch, der Math., 25 (1974), 649-656. Zbl 0297.46006, MR 0374856
Reference: [81] M. Valdivia: Some criteria for weak compactness.J. Reine Angew. Math. 255 (1972), 165-169. Zbl 0239.46001, MR 0300047
Reference: [82] M. Valdivia: On inductive limits of Banach spaces.Manuscr. Math. 15 (1975), 153-163. Zbl 0327.46005, MR 0511660
Reference: [83] M. Valdivia: Localization theorems in webbed spaces.Semesterbericht Tubingen 1982.
Reference: [84] M. Valdivia: On Slowikowski, Raikov and De Wilde's closed graph theorem.(preprint). MR 0849592
Reference: [85] M. Valdivia: On products of Baire spaces.(preprint).
Reference: [86] M. Valdivia: $B_r$-complete spaces which are not $B$-complete.(preprint). MR 0731346
Reference: [87] M. Valdivia: On certain classes of locally convex spaces without $C$-web.Ann. Inst. Fourier, 32 (1982), 261-269. MR 0662446
Reference: [88] M. Valdivia: On countable locally convex direct sums.Arch, der Math. 26 (1975), 407-413. Zbl 0312.46014, MR 0380341
Reference: [89] M. Valdivia: Some new results on bornological barrelled spaces.Proc. Symp. Funct. Anal. Silivri (Istanbul), 1973. MR 0433181
Reference: [90] M. Valdivia P. Pérez Carreras: On totally barreled spaces.Math. Z., 178 (1981), 263-269. MR 0631632
Reference: [91] M. Valdivia P. Pérez Carreras: Sobre espacios (LF) metrizables.Collect. Math, (to b published).
Reference: [92] A. Wilansky: On a characterization of barrelled spaces.Proc. A.M.S. 57 (1976), 375. Zbl 0304.46001, MR 0412761
Reference: [93] J. Diestel: Geometry of Banach spaces-Selected Topics.Lecture Notes in Math. Springer 1975. Zbl 0307.46009, MR 0461094
Reference: [94] S. F. Bellenot E. Dubinsky: Fréchet spaces with nuclear Köthe quotients.(preprint). MR 0667161
Reference: [95] J. Bonet: Representaciones de los espacios $\cal E^K(V, E)$ y $\cal D^K(V, E)$.Rev. Real Acad. Sci. Madrid, 76, (1982), 121-129.
Reference: [96] J. Bonet: Una nota sobre la coincidencia de topologias en productos tensoriales.(preprint).
Reference: [97] J. Bonet: Quojections and projective tensor products.(preprint). Zbl 0557.46003, MR 0807449
Reference: [98] A. Defant W. Govaerts: Tensor products and spaces of vector-valued continuous functions.(peprint).
Reference: [99] V. Moscatelli: Fréchet spaces without continuous norms and without bases.Bull. London Math. Soc. 12 (1980), 63-66. Zbl 0407.46002, MR 0565487
Reference: [100] D. Vogt: Some results on continuous linear mappings between Frechet spaces.Funct. Anal., North Holland 1984. MR 0761391
Reference: [101] D. Vogt: Frecheträume zwischen denen jede stetige lineare Abbildung beschränkt ist.J. Reine Angew. Math. 345, (1983), 182-200. Zbl 0514.46003, MR 0717893
Reference: [102] D. Vogt: Subspaces and quotients of s.Funct. Anal. North Holland 1977. MR 0625306
.

Files

Files Size Format View
CasPestMat_112-1987-2_3.pdf 2.813Mb application/pdf View/Open
Back to standard record
Partner of
EuDML logo