A property of Dunford-Pettis type in topological groups

Proceedings of the American Mathematical Society

Volumn 132, Issue 6, 2004, Pages 1827-1837

  Martin Peinador E ^a   Tarieladze, V ^b  

^a UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

^b INSTITUTE OF PHYSICS   (Georgia)

Author keywords

Bohr topology; Dual group; Dunford Pettis property; Locally convex space; Pontryagin reflexive; Schur property

Indexed keywords

EID: 2442660141     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9939-03-07249-6     Document Type: Conference Paper

References (23)

1. Aussenhofer, L., Contributions to the Duality Theory of Abelian Topological Groups and to the Theory of Nuclear Groups. Dissertationes Mathematicae 384 (1999), 113 pp. MR 2001c:43003
2. Banaszczyk, W., Additive Subgroups of Topological Vector Spaces, Lecture Notes in Mathematics 1466, Springer-Verlag, Berlin, Heidelberg, New York, 1991. MR 93b:46005
3. Banaszczyk, W., and E. Martín-Peinador, The Glicksberg theorem on weakly compact sets for nuclear groups, Annals of the New York Academy of Sciences 788 (1996), 34-39. MR 99e:22001
4. Bombal, F., and I. Villanueva, On the Dunford-Pettis property of the tensor products of C(K) spaces, Proc. Amer. Math. Soc. 129 (2001), 1359-1363. MR 2001h:46024
5. Bruguera, M., Grupos topológicos y grupos de convergencia: estudio de la dualidad de Pontryagin, Doctoral Dissertation, 1999.
6. Cascales, B., and J. Orihuela, On compactness in locally convex spaces, Math. Z. 195 (1987), 365-381. MR 88i:46021
7. Cembranos, P., The hereditary Dunford-Pettis property on C(K, E), Illinois J. Math. 31 (1987), 365-373. MR 88g:46028
8. 1(E), Proc. Amer. Math. Soc. 108 (1990), 947-950. MR 90i:46019
9. Chasco, M. J., Pontryagin duality for metrizable groups, Archiv der Math. 70 (1998), 22-28. MR 98k:22003
10. Chasco, M. J., E. Martín-Peinador, and V. Tarieladze, On Mackey topology for groups, Studia Math. 132 (1999), 257-284. MR 2000b:46003
11. Comfort, W. W., S. Hernández, and F. J. Trigos-Arrieta, Relating a locally compact Abelian group to its Bohr compactification, Advances in Math. 120 (1996), 322-344. MR 97k:22005
12. Comfort, W. W., and K. A. Ross, Topologies induced by groups of characters, Fundamenta Math. 55 (1964), 283-291. MR 30:183
13. Diestel, J., A survey of results related to the Dunford-Pettis property, Contemporary Mathematics 2 (1980), 15-60. MR 82i:46023
14. Diestel, J., Sequences and Series in Banach Spaces, Graduate Texts in Mathematics 92, Springer-Verlag, New York, 1984. MR 85i:46020
15. Dunford, N., and B. J. Pettis, Linear operations on summable functions, Trans. Amer. Math. Soc. 47 (1940), 323-392. MR l:338b
16. Galindo, J., S. Hernández, and S. Macario, A characterization of the Schur property by means of the Bohr topology, Topology and Appl. 97 (1999), 99-108. MR 2000k:22002
17. Glicksberg, I., Uniform boundedness for groups, Canadian Journal of Math. 14 (1962), 269-276. MR 27:5856
18. Grothendieck, A., Sur les applications linéaires faiblement compactes d'espaces du type C(K), Canad. J. Math. 5 (1953), 129-173. MR 15:438b
19. Hewitt, E., and K. A. Ross, Abstract Harmonic Analysis I, Die Grundlehren der Mathematischen Wissenschaften 115, Springer-Verlag, Berlin, 1963. MR 28:158
20. Martín-Peinador, E., A reflexive admissible topological group must be locally compact, Proc. Amer. Math. Soc. 123 (1995), 3563-3566. MR 96a:22002
21. Remus, D., and F. J. Trigos-Arrieta, Abelian groups which satisfy Pontryagin duality need not respect compactness, Proc. Amer. Math. Soc. 117 (4) (1993), 1195-1200. MR 93e:22009
22. Smith, M. F., The Pontryagin duality theorem in linear spaces, Ann. Math. 56 No. 2 (1952), 248-253. MR 14:183a
23. Varopoulos, N. T., Studies in harmonic analysis, Proc. Cambridge Philos. Soc. 60 (1964), 465-516. MR 29:1284