Some aspects of the theory of barreled spaces

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1. N. Adasch B. Ernst D. Keim, Topological Vector Spaces, Springer, 1978. (1978) MR0487376
2. I. Amemiya Y. Komura, Über nicht-vollständige Montelräume, Math. Ann. 177 (1968), 273-277. (1968) MR0232182
3. D. Amir J. Lindenstrauss, The structure of weakly compact sets in Banach space 
4. J. Arias, Dense hyperplanes of first category, Math. Ann., 249 (1980), 111-114. (1980) Zbl0419.46015MR0578718
5. J. Arias, Normed barely Baire spaces, Israel J. Math., 42 (1982), 33 - 36. (1982) Zbl0495.46004MR0687932
6. J. Arias, $l_0^{\infty }\left(\Sigma \right)$ no es totalmente tonelado, Rev. Real Acad. Ci. Madrid (to be published). 
7. J. Bait P. Dierolf J. Voigt, Summable sequences and topological properties of $m\left(l\right)$, Arch. d. Math. 
8. Y. Benyamini M. E. Rudin M. Wage, Continuous images of weakly compact subsets of Banach spaces, Pacific J. Math. (1977). (1977) MR0625889
9. J. Bonet P. Perez Carreras, Some results on barreledness in projective tensor products, Math. Z., 185 (1984), 333-338. (1984) MR0731681
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. (1982) MR0705014
11. J. Bonet P. Pérez Carreras, Remarks on the stability of barreled-type topologies, Bull. Soc. Roy. Sci. Liege, 52 (1983), 313-318. (1983) MR0731286
12. M. De Wilde, Vector topologies and linear maps on products of topological vector spaces, Math. Ann., 196 (1972), 117-128. (196) MR0298374
13. M. De Wilde, Closed graph theorems and webbed spaces, Pitman, 1978. (1978) Zbl0373.46007
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. (1972) MR0312187
15. S. Dierolf, A note on the lifting of linear and locally convex topologies on a quotient space, Collect. Math., 31 (1980), 60-62. (1980) Zbl0453.46002MR0621724
16. J. Dieudonné, Sur les propriétés de permanence de certain espaces vectoriels topolgiques, Ann. Soc. Polon. Math., 25 (1952), 50-55 (1953). (1952) MR0056189
17. L. Drewnowski, Un theoreme sur les operateurs de $l^{\infty }\left(\Gamma \right)$, C.R. Acad. Sci. Paris t. 281, serie A-967. MR0385626
18. P. Dierolf S. Dierolf L. Drewnowski, Remarks and examples concerning unordered-Baire-like spaces and ultrabarrelled spaces, Coll. Math. 39 110-117. 
19. N. Dunford J. Schwartz, Linear Operators Vol. 1, Interscience 1958. (1958) 
20. V. Eberhardt, Über Komuras Graphenstaz: Vollständigkeit, Permanenzeigenschaften und Beispiele, Habilitationsschrift, München 1977. (1977) 
21. M. Eidelheit, Zur Theorie der Systeme linearer Gleichungen, Studia Math., 6 (1936), 139-148. (1936) Zbl0015.35603
22. K. Floret, Folgenretraktive Sequenzen lokalkonvexer Räume, J. Reine u. Angew. Math., 259 (1973), 65-85. (1973) Zbl0251.46003MR0313748
23. Grothendieck A., Produits tensoriels topologiques, Mem. A.M.S. 16 1955. (1955) Zbl0123.30301MR0075539
24. A. Grotendieck, Sur les espaces (F) et (DF), Summa Brasil. Math. 3, (1954), 57-121. (1954) MR0075542
25. C. Harvey, F. R., Open mappings and the lack of fully completeness of $D^{\text{'}}\left(\Omega \right)$, Proc. A.M.S. 25 (1970), 786-790. (1970) Zbl0197.39101MR0265906
26. R. Hollstein, Über die Tonneliertheit von lokalkonvexen Tensorprodukten, Manusc. Math., 22 (1977), 7-12. (1977) Zbl0359.46046MR0482032
27. J. Horvath, Topological Vector Spaces and Distributions, Vol I, Addison-Wesley 1966. (1966) Zbl0143.15101MR0205028
28. H. Jarchow, Locally Convex Spaces, Teubner 1981. (1981) Zbl0466.46001MR0632257
29. J. Izquierdo, Sobre ciertas clases de espacios hipertonelados, Tesis Doctoral, Valencia 1982. (1982) 
30. N. Kalton, Some forms of the closed graph theorem, Proc. Cambridge Phil. Soc., 70 (1971), 401-408. (1971) Zbl0221.46006MR0301476
31. J. L. Kelley I. Namioka, Linear Topological Spaces, van Nostrand 1963. (1963) MR0166578
32. Y. Komura, On linear topological spaces, Kumamoto J. Sci. Ser. A 5 (1962), 148-157. (1962) Zbl0105.30803MR0151817
33. G. Köthe, Topologische Lineare Raume I, Springer 1966. (1966) MR0194863
34. G. Köthe, Topological Vector Spaces II, Springer 1979. (1979) MR0551623
35. M. Mahowald, Barrelled spaces and the closed graph theorem, J. London Math. Soc, 36 (1961), 108- 110. (1961) Zbl0097.09001MR0125426
36. B. M. Makarov, On some pathological properties of inductive limits of Banach spaces, (russian). Uspehi Math. Nauk, 18, Nr. 111, (1963), 171-178. (1963) MR0152867
37. A. Marquina, A note on the closed graph theorem, Arch. der Math. 28 (1977), 82-85. (1977) Zbl0351.46003MR0430726
38. A. Marquina J. M. Sanz Serna, Barrelledness conditions on $c_0\left(E\right)$, Arch. der Math., 31 (1978), 589-596. (1978) MR0531574
39. J. M. Mazón, Some classes of locally convex spaces, Arch. der Math. 38 (1982), 131-137. (1982) MR0650344
40. E. Michael M. E. Rudin, A note on Eberlein compacts, Pacific J. Math., 72 (1977), 487-495. (1977) MR0478092
41. A. Moltó, On uniform boundedness properties in exhausting additive set function spaces, Proc Roy. Soc. Edinburgh, 90 A (1981), 175-184. (1981) MR0636071
42. J. Motos, Resultados en dos nuevas clases de espacios localmente convexos, Tesis Doctoral, Valencia 1974. (1974) 
43. V. Moscatelli, Sur une classe d'espaces localment convexes B-complets, C.R. Acad. Sci., Paris, A. 276 (1973), 1205-1208. (1973) MR0324362
44. M. Oberguggenberger, Der Grapehnsatz in lokalkonvexen topologischen Vektorräumen, Teubner-Texte Band 44, 1982. (1982) MR0685147
45. P. Pérez Carreras, Una nota sobre espacios DF, Rev Real Acad. Ci. Madrid, 75 (1981), 739-741. (1981) MR0650044
46. P. Pérez Carreras, Sobre ciertas clases de espacios vectoriales topologicos, Rev. Real Acad. Ci. Madrid, 76 (1982), 585-594. (1982) 
47. P. Pérez Carreras J. Bonet, Remarks and examples concerning suprabarreled and totally barreled spaces, Arch, der Math., 39 (1982), 340-347. (1982) MR0684404
48. P. Pérez Carreras J. Bonet, Espacios Tonelados, Public. Univ. Sevilla 1980. (1980) 
49. A. Pietsch, Nuclear Locally convex Spaces, Springer 1972. (1972) Zbl0308.47024MR0350360
50. J. O. Popoola I. Tweddle, Density character, barrelledness and the closed graph theorem, Coll, Math., 40 (1979), 249-258. (1979) MR0547867
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. (1953) MR0064303
52. V. Pták, Completeness and the open mapping theorem, Bull. Soc Math. France, 86 (1958), 41-74. (1958) MR0105606
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. (1961) MR0220038
54. D. A. Raikov, Double closed-graph theorem for topological linear spaces, Siber. math. J., 7 (1966), 287-300. (1966) Zbl0171.10701MR0198196
55. W. Roelcke S. Dierolf, On the three-space-problem for topological vector spaces, Collect. Math., 32(1981), 13-35. (1981) MR0643398
56. H. P. Rosenthal, On relatively disjoint families of measures with some applications to Banach space theory, Studia Math., 37 (1970), 13 - 36. (1970) Zbl0227.46027MR0270122
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). (1980) MR0580250
58. H. Saiflu I. Tweddle, The domain spaces for Marquina's closed graph theorem, Archiv der Math., 34 (1980), 463-468. (1980) MR0593773
59. S. Saxon, Some normed barreled spaces which are not Baire, Math. Ann., 209 (1974), 153-160. (1974) MR0352925
60. S. Saxon, Two characterizations of linear Baire spaces, Proc. A.M.S., 45, (1974). (1974) Zbl0294.46003MR0358274
61. S. Saxon, Nuclear and product spaces, Baire-like spaces and the strongest locally convex topology, Math. Ann., 197 (1972), 87-106. (197) MR0305010
62. S. Saxon M. Levin, Every countable-codimensional subspace of a barrelled space is barrelled, Proc. A.M.S., 29 (1971), 91-96. (1971) MR0280972
63. S. Saxon P. Narayanaswami, Metrizable (LF)-spaces, (db)-spaces and the separable quotient problem, Bull. Austral. Math. Soc., 23 (1981), 65-80. (1981) MR0615133
64. S. Saxon A. Wilansky, The equivalence of some Banach space problems, Coll. Math., 37 (1977), 217-226. (1977) MR0511780
65. W. Slowikowski, Quotient spaces and the open map theorem, Bull. A.M.S., 67 (1961), 498-500. (1961) Zbl0100.32601MR0131743
66. J. Schmets, Espaces de fonctions continues, Lect. Notes in Math. 519, Springer 1976. (1976) Zbl0334.46022MR0423058
67. E. T. Shavgulidze, On the hypercompleteness of locally convex spaces, Math. Notes 13 (1973), 180-182. (1973) MR0344839
68. E. T. Shavgulidze, Br-completeness, Funct. Anal. Appl. 9 (1975), 363-364. (1975) 
69. O. K. Smoljanov, The space D is not hereditarily complete, Math. USSR, Izvestija 5 (1971), 696-710. (1971) 
70. A. Todd S. Saxon, A property of locally convex Baire spaces, Math. Ann., 206 (1973), 23-32. (1973) MR0328523
71. I. Tweddle F. E. Yeomans, On the stability of barrelled topologies II, Glasgow Math. J., 21 (1980), 91-95. (1980) MR0558281
72. M. Valdivia, On certain normed barrelled spaces, Ann. Inst. Fourier, 29 (1979), 39-56. (1979) MR0552959
73. M. Valdivia, Topics in Locally Convex Spaces, North Holland 1982. (1982) Zbl0489.46001MR0671092
74. M. Valdivia, Absolutely convex sets in barrlled spaces, Ann. Inst. Fourier, 21 (1971), 3-13. (1971) MR0333643
75. M. Valdivia, On suprabarreled spaces, Proc. Funct. Anal., holomorphy and approx. theory (Rio de Janeiro 1978) Lect. Notes in Math. 843 Springer 1981. (1978) MR0610847
76. M. Valdivia, The space of distributions $D^{\text{'}}\left(\Omega \right)$ is not $B_r$-complete, Math. Ann., 211 (1974), 145-149. (1974) Zbl0288.46033MR0370177
77. M. Valdivia, On $B_r$-completeness, Ann. Inst. Fourier, 25 (1975), 29-43. (1975) Zbl0301.46004MR0399792
78. M. Valdivia, [unknown], Ann. Inst. Fourier 27 (1977), 29-43. (1977) MR0477665
79. M. Valdivia, Some examples on quasi-barrelled spaces, Ann. Inst. Fourier, 22 (1972), 21-26. (1972) Zbl0226.46005MR0336277
80. M. Valdivia, Mackey convergence and the closed graph theorem, Arch, der Math., 25 (1974), 649-656. (1974) Zbl0297.46006MR0374856
81. M. Valdivia, Some criteria for weak compactness, J. Reine Angew. Math. 255 (1972), 165-169. (1972) Zbl0239.46001MR0300047
82. M. Valdivia, On inductive limits of Banach spaces, Manuscr. Math. 15 (1975), 153-163. (1975) Zbl0327.46005MR0511660
83. M. Valdivia, Localization theorems in webbed spaces, Semesterbericht Tubingen 1982. (1982) 
84. M. Valdivia, On Slowikowski, Raikov and De Wilde's closed graph theorem, (preprint). MR0849592
85. M. Valdivia, On products of Baire spaces, (preprint). 
86. M. Valdivia, $B_r$-complete spaces which are not $B$-complete, (preprint). MR0731346
87. M. Valdivia, On certain classes of locally convex spaces without $C$-web, Ann. Inst. Fourier, 32 (1982), 261-269. (1982) MR0662446
88. M. Valdivia, On countable locally convex direct sums, Arch, der Math. 26 (1975), 407-413. (1975) Zbl0312.46014MR0380341
89. M. Valdivia, Some new results on bornological barrelled spaces, Proc. Symp. Funct. Anal. Silivri (Istanbul), 1973. (1973) MR0433181
90. M. Valdivia P. Pérez Carreras, On totally barreled spaces, Math. Z., 178 (1981), 263-269. (1981) MR0631632
91. M. Valdivia P. Pérez Carreras, Sobre espacios (LF) metrizables, Collect. Math, (to b published). 
92. A. Wilansky, On a characterization of barrelled spaces, Proc. A.M.S. 57 (1976), 375. (1976) Zbl0304.46001MR0412761
93. J. Diestel, Geometry of Banach spaces-Selected Topics, Lecture Notes in Math. Springer 1975. (1975) Zbl0307.46009MR0461094
94. S. F. Bellenot E. Dubinsky, Fréchet spaces with nuclear Köthe quotients, (preprint). MR0667161
95. J. Bonet, Representaciones de los espacios ${ℰ}^K(V,E)$ y ${𝒟}^K(V,E)$, Rev. Real Acad. Sci. Madrid, 76, (1982), 121-129. (1982) 
96. J. Bonet, Una nota sobre la coincidencia de topologias en productos tensoriales, (preprint). 
97. J. Bonet, Quojections and projective tensor products, (preprint). Zbl0557.46003MR0807449
98. A. Defant W. Govaerts, Tensor products and spaces of vector-valued continuous functions, (peprint). 
99. V. Moscatelli, Fréchet spaces without continuous norms and without bases, Bull. London Math. Soc. 12 (1980), 63-66. (1980) Zbl0407.46002MR0565487
100. D. Vogt, Some results on continuous linear mappings between Frechet spaces, Funct. Anal., North Holland 1984. (1984) MR0761391
101. D. Vogt, Frecheträume zwischen denen jede stetige lineare Abbildung beschränkt ist, J. Reine Angew. Math. 345, (1983), 182-200. (1983) Zbl0514.46003MR0717893
102. D. Vogt, Subspaces and quotients of s, Funct. Anal. North Holland 1977. (1977) MR0625306