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Book Information:
Authors:
J. C. Ferrando,
M. López Pellicer and
L. M. Sánchez Ruiz
Title:
Metrizable barrelled spaces
Additional book information:
Pitman Res. Notes in Math. Ser., vol. 332, Longman,
1995,
238 pp.,
ISBN 0-582-28703-0,
$30.00$
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
Susanne Dierolf and Jerzy Kąkol, On S-barrelled spaces, Results Math. 28 (1995), no. 1-2, 40–48. MR 1345353, DOI 10.1007/BF03322238
J. Diestel and B. Faires, On vector measures, Trans. Amer. Math. Soc. 198 (1974), 253–271. MR 350420, DOI 10.1090/S0002-9947-1974-0350420-8
Juan Carlos Díaz, Miguel Florencio, and Pedro J. Paúl, A uniform boundedness theorem for $L^\infty (\mu , E)$, Arch. Math. (Basel) 60 (1993), no. 1, 73–78. MR 1193096, DOI 10.1007/BF01194241
Lech Drewnowski, Miguel Florencio, and Pedro J. Paúl, The space of Pettis integrable functions is barrelled, Proc. Amer. Math. Soc. 114 (1992), no. 3, 687–694. MR 1107271, DOI 10.1090/S0002-9939-1992-1107271-2
L. Drewnowski, M. Florencio, and P. J. Paúl, Uniform boundedness of operators and barrelledness in spaces with Boolean algebras of projections, Atti Sem. Mat. Fis. Univ. Modena 41 (1993), no. 2, 317–329. MR 1248001
Lech Drewnowski, Miguel Florencio, and Pedro J. Paúl, On the barrelledness of spaces of bounded vector functions, Arch. Math. (Basel) 63 (1994), no. 5, 449–458. MR 1300741, DOI 10.1007/BF01196676
Francisco J. Freniche, Barrelledness of the space of vector valued and simple functions, Math. Ann. 267 (1984), no. 4, 479–486. MR 742894, DOI 10.1007/BF01455966
J. Kąkol and W. Roelcke, On the barrelledness of $l^p$-direct sums of seminormed spaces for $1\leq p\leq \infty$, Arch. Math. (Basel) 62 (1994), no. 4, 331–334. MR 1264704, DOI 10.1007/BF01201785
Michael Kunzinger, Barrelledness, Baire-like- and $(LF)$-spaces, Pitman Research Notes in Mathematics Series, vol. 298, Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1993. MR 1267058
12. P. Pérez Carreras, J. Bonet, Barrelled locally convex spaces, Math. Studies, North-Holland, 1987.
13. F. Rothberger, Sur un ensemble toujours de premiére catégorie qui est dépourvu de la propriéte 
, Fund. Math. 32 (1939), 294-300.
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
Stephen A. Saxon, Two characterizations of linear Baire spaces, Proc. Amer. Math. Soc. 45 (1974), 204–208. MR 358274, DOI 10.1090/S0002-9939-1974-0358274-6
T. Venkatarayudu, The $7$-$15$ problem, Proc. Indian Acad. Sci., Sect. A. 9 (1939), 531. MR 0000001, DOI 10.1090/gsm/058
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
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
Manuel Valdivia and Pedro Pérez Carreras, On totally barreled spaces, Math. Z. 178 (1981), no. 2, 263–269. MR 631632, DOI 10.1007/BF01262043
M. Valdivia, Products of Baire topological vector spaces, Fund. Math. 125 (1985), no. 1, 71–80. MR 813990, DOI 10.4064/fm-125-1-71-80
Manuel Valdivia, Topics in locally convex spaces, Notas de Matemática [Mathematical Notes], vol. 85, North-Holland Publishing Co., Amsterdam-New York, 1982. MR 671092
M. Valdivia, Classes of barrelled spaces related with the closed graph theorem, Portugal. Math. 40 (1981), no. 3, 345–366 (1985). MR 819901
- 1.
- I. Amemiya, Y. Komura, Über nicht vollständige Montelräume, Math. Ann. 177 (1968), 273-277. MR 38:508
- 2.
- J. Arias de Reyna, Dense hyperplanes of first category, Math. Ann. 249 (1980), 111-114. MR 81g:46019
- 3.
- S. Dierolf, J. Kakol, On s-barrelled spaces, Results in Math. 28 (1995), 40-48. MR 96f:46002
- 4.
- J. Diestel, B. Faires, On vector measures, Trans. Amer. Math. Soc. 198 (1974), 253-271. MR 50:2912
- 5.
- J. C. Diaz, M. Florencio, J. P. Paúl, A uniform boundedness theorem for
, Arch. Math. 60 (1993), 73-78. MR 94f:46037
- 6.
- L. Drewnowski, M. Florencio, P. J. Paúl, The space of Pettis integrable functions is barrelled, Proc. Amer. Math. Soc. 114 (1992), 687-694. MR 92f:46045
- 7.
- L. Drewnowski, M. Florencio, P. J. Paúl, Uniform boundedness of operators and barrelledness in spaces with Boolean algebras of projections, Atti. Sem. Math. Fis. Univ. Modena 41 (1993), 317-329. MR 94m:46004
- 8.
- L. Drewnowski, M. Florencio, P. J. Paúl, On the barrelledness of spaces of bounded vector functions, Arch. Math. 63 (1994), 449-458. MR 95i:46047
- 9.
- F. J. Freniche, Barrelledness conditions of the space of vector valued and simple functions, Math. Ann. 267 (1984), 479-489. MR 85f:46074
- 10.
- J. Kakol, W. Roelcke, On the barrelledness of
-direct sums of seminormed spaces for 
, Arch. Math. 62 (1994), 331-334. MR 95f:46002
- 11.
- M. Kunzinger, Barrelledness, Baire-like and (LF)-spaces, Pitman Research Notes in Math., Longman, 1993. MR 95e:46004
- 12.
- P. Pérez Carreras, J. Bonet, Barrelled locally convex spaces, Math. Studies, North-Holland, 1987.
- 13.
- F. Rothberger, Sur un ensemble toujours de premiére catégorie qui est dépourvu de la propriéte , Fund. Math. 32 (1939), 294-300.
- 14.
- S. A. Saxon, Nuclear and product spaces, Baire-like spaces and the strongest locally convex topology, Math. Ann. 197 (1972), 87-106. MR 46:4140
- 15.
- S. A. Saxon, Two characterizations of linear Baire spaces, Proc. Amer. Math. Soc. 45 (1974), 204-208. MR 50:10740
- 16.
- S. A. Saxon, L. M. Sánchez-Ruiz, Barrelled countable enlargements and the bounding cardinal, J. London Math. Soc. 53 (1996), 158-166. MR 1:362 693
- 17.
- S. A. Saxon, A. Wilansky, The equivalence of some Banach space problems, Coll. Math. 37 (1977), 217-226. MR 0511780
- 18.
- S. A. Saxon, M. Levin, Every countable-codimensional subspace of a barrelled space is barrelled, Proc. Amer. Math. Soc. 29 (1971), 91-96. MR 43:6691
- 19.
- M. Valdivia, P. Pere\'{z} Carreras, On totally barrelled spaces, Math. Z. 178 (1981), 263-269. MR 82m:46002
- 20.
- M. Valdivia, Products of Baire topological vector spaces, Fund. Math. 125 (1985), 61-80. MR 87d:46007
- 21.
- M. Valdivia, Topics in locally convex spaces, Math. Studies, North-Holland, 1982. MR 84i:46007
- 22.
- M. Valdivia, Classes of barrelled spaces related with the closed graph theorem, Portugaliae Math. 40 (1981), 345-366. MR 87g:46009
Review Information:
Reviewer:
Jerzy Ka̧kol
Affiliation:
Poznań University
Email:
kakol@math.amu.edu.pl
Journal:
Bull. Amer. Math. Soc.
34 (1997), 101-105
DOI:
https://doi.org/10.1090/S0273-0979-97-00706-4
Review copyright:
© Copyright 1997
American Mathematical Society
