Bulletin of the American Mathematical Society

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Book Information:

Authors: P. Pérez Carreras and J. Bonet
Title: Barrelled locally convex spaces
Additional book information: North-Holland Math. Stud., vol. 131, (L. Nachbin, ed.), North-Holland, Amsterdam, New York, Oxford, Tokyo, 1987, xv+512 pp., $80.00. ISBN 0-444-70129-X.

Ichiro Amemiya and Yukio K\B{o}mura, Über nicht-vollständige Montelräume, Math. Ann. 177 (1968), 273–277 (German). MR 232182, DOI 10.1007/BF01350719

J. Arias de Reyna, Dense hyperplanes of first category, Math. Ann. 249 (1980), no. 2, 111–114. MR 578718, DOI 10.1007/BF01351408

3.

K. D. Bierstedt, A previous review of Barrelled Locally Convex Spaces, MR 88j #46003.

4.

M. De Wilde, Quelques théorèmes d'extension de fonctionelles lineaires, Bull. Soc. Royale Sci. Liége 9-10 (1966), 551-557.

5.

S. Dierolf, Über Vererbarkeitseigenschaften in topologischen Vectorräumen, dissertation, München, 1974..

L. Drewnowski, Quasicomplements in $F$-spaces, Studia Math. 77 (1984), no. 4, 373–391. MR 741453, DOI 10.4064/sm-77-4-373-391

7.

M. Eidelheit, Zur theorie der systeme lineares gleichungen, Studia Math. 6 (1936), 139-148.

J. C. Ferrando and M. López Pellicer, Quasi-suprabarrelled spaces, J. Austral. Math. Soc. Ser. A 46 (1989), no. 1, 137–145. MR 966290

John Horváth, Topological vector spaces and distributions. Vol. I, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1966. MR 0205028

S. Karlin, Bases in Banach spaces, Duke Math. J. 15 (1948), 971–985. MR 29103

Gottfried Köthe, Topological vector spaces. I, Die Grundlehren der mathematischen Wissenschaften, Band 159, Springer-Verlag New York, Inc., New York, 1969. Translated from the German by D. J. H. Garling. MR 0248498

Pedro Pérez Carreras and José Bonet, Note on a result of Eidelheit, Collect. Math. 33 (1982), no. 2, 195–200 (Spanish). MR 719289

Pedro Pérez Carreras and José Bonet, Remarks and examples concerning suprabarreled and totally barreled spaces, Arch. Math. (Basel) 39 (1982), no. 4, 340–347. MR 684404, DOI 10.1007/BF01899442

W. J. Robertson, On properly separable quotients of strict (LF) spaces, J. Austral. Math. Soc. Ser. A 47 (1989), no. 2, 307–312. MR 1008844

Wendy Robertson, On the closed graph theorem and spaces with webs, Proc. London Math. Soc. (3) 24 (1972), 692–738. MR 306857, DOI 10.1112/plms/s3-24.4.692

W. J. Robertson, S. A. Saxon, and A. P. Robertson, Barrelled spaces and dense vector subspaces, Bull. Austral. Math. Soc. 37 (1988), no. 3, 383–388. MR 943441, DOI 10.1017/S0004972700027003

I. Tweddle and F. E. Yeomans, On the stability of barrelled topologies. II, Glasgow Math. J. 21 (1980), no. 1, 91–95. MR 558281, DOI 10.1017/S0017089500004043

Stephen A. Saxon, Nuclear and product spaces, Baire-like spaces, and the strongest locally convex topology, Math. Ann. 197 (1972), 87–106. MR 305010, DOI 10.1007/BF01419586

19.

S. A. Saxon, Barrelled spaces E with card (E') ≤ dim (E), (in preparation).

20.

S. A. Saxon. Affirming the three-space problem for ℓ, (in preparation).

21.

S. A. Saxon, Fréchet, Banach and other quotients of (LF)-, (LN)-and other spaces by limit subspaces (in preparation).

22.

S. A. Saxon, Every countable-codimensional subspace of an infinite-dimensional [non-normable] Fréchet space has an infinite-dimensional Fréchet quotient [isomorphic to ω], Bull. Polish Acad. Sci. Math. 2 (1991).

Stephen A. Saxon, All separable Banach spaces are quotients of any countable-codimensional subspace of $l_1$, Bull. Polish Acad. Sci. Math. 39 (1991), no. 3-4, 167–173. MR 1194485

S. A. Saxon, The codensity character of topological vector spaces, Topological vector spaces, algebras and related areas (Hamilton, ON, 1994) Pitman Res. Notes Math. Ser., vol. 316, Longman Sci. Tech., Harlow, 1994, pp. 24–36. MR 1319370

25.

S. A. Saxon, The fit and flat components of barrelled spaces, (in preparation).

26.

S. A. Saxon, The questions of (LF)-space dominance: (u) d,b or not (u)d,b, (in preparation).

27.

S. A. Saxon, Non-Baire hyperplanes in non-separable Baire spaces (in preparation).

Stephen A. Saxon, A maximal extension of Köthe’s homomorphism theorem, Note Mat. 12 (1992), 229–236. Dedicated to the memory of Professor Gottfried Köthe. MR 1258576

29.

S. A. Saxon, Limit subspaces and the strongest locally convex topology (in preparation).

Stephen Saxon and Mark Levin, Every countable-codimensional subspace of a barrelled space is barrelled, Proc. Amer. Math. Soc. 29 (1971), 91–96. MR 280972, DOI 10.1090/S0002-9939-1971-0280972-0

Stephen A. Saxon and P. P. Narayanaswami, Metrizable (LF)-spaces, (db)-spaces, and the separable quotient problem, Bull. Austral. Math. Soc. 23 (1981), no. 1, 65–80. MR 615133, DOI 10.1017/S0004972700006900

P. P. Narayanaswami and Stephen A. Saxon, (LF)-spaces, quasi-Baire spaces and the strongest locally convex topology, Math. Ann. 274 (1986), no. 4, 627–641. MR 848508, DOI 10.1007/BF01458598

Stephen A. Saxon and P. P. Narayanaswami, Metrizable [normable] $(\textrm {LF})$-spaces and two classical problems in Fréchet [Banach] spaces, Studia Math. 93 (1989), no. 1, 1–16. MR 989565, DOI 10.4064/sm-93-1-1-16

Stephen A. Saxon and Wendy J. Robertson, Dense barrelled subspaces of uncountable codimension, Proc. Amer. Math. Soc. 107 (1989), no. 4, 1021–1029. MR 990433, DOI 10.1090/S0002-9939-1989-0990433-2

Stephen A. Saxon and Albert Wilansky, The equivalence of some Banach space problems, Colloq. Math. 37 (1977), no. 2, 217–226. MR 511780, DOI 10.4064/cm-37-2-217-226

Aaron R. Todd and Stephen A. Saxon, A property of locally convex Baire spaces, Math. Ann. 206 (1973), 23–34. MR 328523, DOI 10.1007/BF01431526

I. Tweddle, Barrelled spaces whose bounded sets have at most countable dimension, J. London Math. Soc. (2) 29 (1984), no. 2, 276–282. MR 744098, DOI 10.1112/jlms/s2-29.2.276

M. Valdivia, Fréchet spaces generated by weakly compact subsets, Collect. Math. 38 (1987), no. 1, 17–25 (Spanish, with English summary). MR 970631

Manuel Valdivia, On suprabarrelled spaces, Functional analysis, holomorphy, and approximation theory (Proc. Sem., Univ. Fed. Rio de Janeiro, Rio de Janeiro, 1978) Lecture Notes in Math., vol. 843, Springer, Berlin, 1981, pp. 572–580. MR 610847

M. Valdivia, On Baire-hyperplane spaces, Proc. Edinburgh Math. Soc. (2) 22 (1979), no. 3, 247–255. MR 560987, DOI 10.1017/S0013091500016412

Manuel Valdivia, A property of Fréchet spaces, Functional analysis, holomorphy and approximation theory, II (Rio de Janeiro, 1981) North-Holland Math. Stud., vol. 86, North-Holland, Amsterdam, 1984, pp. 469–477. MR 771341, DOI 10.1016/S0304-0208(08)70841-7

Manuel Valdivia and Pedro Pérez Carreras, On totally barreled spaces, Math. Z. 178 (1981), no. 2, 263–269. MR 631632, DOI 10.1007/BF01262043

1.

I. Amemiya and Y. Kōmura, Über nicht-vollständige Montelräume, Math. Ann. 177 (1968), 273-277. MR 0232182

2.

Arias de Reyna, Dense hyperplanes of first category, Math. Ann. 249 (1980), 111-114. MR 578718

3.

K. D. Bierstedt, A previous review of Barrelled Locally Convex Spaces, MR 88j #46003.

4.

M. De Wilde, Quelques théorèmes d'extension de fonctionelles lineaires, Bull. Soc. Royale Sci. Liége 9-10 (1966), 551-557.

5.

S. Dierolf, Über Vererbarkeitseigenschaften in topologischen Vectorräumen, dissertation, München, 1974..

6.

L. Drewnowski, Quasicomplements in (F)-spaces, Studia Math. 77 (1984), 373-391. MR 741453

7.

M. Eidelheit, Zur theorie der systeme lineares gleichungen, Studia Math. 6 (1936), 139-148.

8.

J. Ferrando and M. López-Pellicer, Quasi-suprabarrelled spaces, J. Austral. Math. Soc. Ser. A 46 (1989), 137-145. MR 966290

9.

J. M. Horváth, Topological Vector Spaces and Distributions, vol. I, Addison-Wesley, Reading, MA, 1966. MR 205028

10.

S. Karlin, Bases in Banach spaces, Duke Math. J. 15 (1948), 971-985. MR 29103

11.

G. Köthe, Topological Vector Spaces I, Springer-Verlag, Berlin, 1969. MR 248498

12.

P. Pérez Carreras and J. Bonet, Una nota sobre un resultado de Eidelheit, Collectanea Math. 33 (1982), 195-199. MR 719289

13.

P. Pérez Carreras and J. Bonet, Remarks and examples concerning suprabarrelled and totally barrelled spaces, Arch. Math. 39 (1982), 340-347. MR 684404

14.

W. J. Robertson, On properly separable quotients of strict (LF)-spaces, J. Austral. Math. Soc. Ser. A 47 (1989), 307-312. MR 1008844

15.

A. P. Robertson and W. J. Robertson, On the closed graph theorem, Proc. Glasgow Math. Soc. 3 (1956), 692-738. MR 306857

16.

W. J. Robertson, S. A. Saxon and A. P. Robertson, Barrelled spaces and dense vector subspaces, Bull. Austral. Math. Soc. 37 (1988), 383-388. MR 943441

17.

W. J. Robertson, I. Tweddle, and F. E. Yeomans, On the stability of barrelled topologies III, Bull. Austral. Math. Soc. 22 (1980), 99-112. MR 589939

18.

S. A. Saxon, Nuclear and product spaces, Baire-like spaces, and the strongest locally convex topology, Math. Ann. 197 (1972), 87-106. MR 305010

19.

S. A. Saxon, Barrelled spaces E with card (E') ≤ dim (E), (in preparation).

20.

S. A. Saxon. Affirming the three-space problem for ℓ, (in preparation).

21.

S. A. Saxon, Fréchet, Banach and other quotients of (LF)-, (LN)-and other spaces by limit subspaces (in preparation).

22.

S. A. Saxon, Every countable-codimensional subspace of an infinite-dimensional [non-normable] Fréchet space has an infinite-dimensional Fréchet quotient [isomorphic to ω], Bull. Polish Acad. Sci. Math. 2 (1991).

23.

S. A. Saxon, All separable Banach spaces are quotients of any countable-codimensional subspace of ℓ, Bull. Polish Acad. Sci. Math. 2 (1991). MR 1194485

24.

S. A. Saxon, The codensity character of topological vector spaces, (in preparation). MR 1319370

25.

S. A. Saxon, The fit and flat components of barrelled spaces, (in preparation).

26.

S. A. Saxon, The questions of (LF)-space dominance: (u) d,b or not (u)d,b, (in preparation).

27.

S. A. Saxon, Non-Baire hyperplanes in non-separable Baire spaces (in preparation).

28.

S. A. Saxon, A maximal extension of Köthe's homomorphism theorem, special "Köthe" volume of Note Mat. (to appear). MR 1258576

29.

S. A. Saxon, Limit subspaces and the strongest locally convex topology (in preparation).

30.

S. Saxon and M. Levin, Every countable-codimensional subspace of a barrelled space is barrelled, Proc. Amer. Math. Soc. 29 (1971), 91-96. MR 280972

31.

S. A. Saxon and P. P. Narayanaswami, (LF)-spaces, (db)-spaces and the separable quotient problem, Bull. Austral. Math. Soc. 23 (1981), 65-80. MR 615133

32.

S. A. Saxon and P. P. Narayanaswami, (LF)-spaces, quasi-Baire spaces and the strongest locally convex topology, Math. Ann. 274 (1986), 627-641. MR 848508

33.

S. A. Saxon and P. P. Narayanaswami, Metrizable [normable] (LF)-spaces and two classical problems in Fréchet [Banach] spaces, Studia Math. 93 (1989), 1-16. MR 989565

34.

S. A. Saxon and W. J. Robertson, Dense barrelled subspaces of uncountable codimension, Proc. Amer. Math. Soc. 107 (1989), 1021-1029. MR 990433

35.

S. A. Saxon and A. Wilansky, The equivalence of some Banach space problems, Colloq. Math. 37 (1977), 217-226. MR 511780

36.

A. R. Todd and S. A. Saxon, A property of locally convex Baire spaces, Math. Ann. 206 (1973), 23-34. MR 328523

37.

I. Tweddle, Barrelled spaces whose bounded sets have at most countable dimension, J. London Math. Soc. 29 (1989), 276-282. MR 744098

38.

M. Valdivia, Sobre ciertos subespacios de primera categoria en espacios vectoriales topológicos de Baire, Collect. Math. 34 (1983), 287-296. MR 970631

39.

M. Valdivia, On suprabarrelled spaces, Functional Anal., Holomorphy and Approx. Theory (G. I. Zapata, ed.), Lecture Notes in Math., vol. 843, Springer-Verlag, New York, 1981, pp. 572-580. MR 610847

40.

M. Valdivia, On Baire-hyperplane spaces, Proc. Edinburgh Math. Soc. 22 (1979), 247-255. MR 560987

41.

M. Valdivia, A property of Fréchet spaces, Functional Anal., Holomorphy and Approx. Theory (G. I. Zapata, ed.), North-Holland Math. Stud., vol. 86, North-Holland, Amsterdam, 1984, pp. 469-477. MR 771341

42.

M. Valdivia and P. Pérez Carreras, On totally barrelled spaces, Math. Z. 178 (1981), 263-269. MR 631632