On Mackey topology for groups

Studia Mathematica

Volumn 132, Issue 3, 1999, Pages 257-284

  Chasco, M J ^a   Martin Peinador E ^c   Tarieladze, V ^b  

^a UNIVERSITY OF NAVARRA   (Spain)

^b INSTITUTE OF PHYSICS   (Georgia)

^c UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

Author keywords

Continuous character; Locally convex space; Locally quasi convex group; Mackey topology; Weakly compact

Indexed keywords

EID: 0040715708     PISSN: 00393223     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (27)

1. W. Banaszczyk, Additive Subgroups of Topological Vector Spaces, Lecture Notes in Math. 1466, Springer, Berlin, 1991.
2. W. Banaszczyk and E. Martín-Peinador, The Glicksberg theorem on weakly compact sets for nuclear groups, in: Ann. New York Acad. Sci. 788, 1996, 34-39.
3. N. Bourbaki, Espaces vectoriels topologiques, Masson, Paris, 1981.
4. M. Bruguera, Some properties of locally quasi-convex groups, Topology Appl. 77 (1997), 87-94.
5. M. J. Chasco and E. Martín-Peinador, Pontryagin reflexive groups are not determined by their continuous characters, Rocky Mountain J. Math. 28 (1998), 155-160.
6. W. W. Comfort and K. A. Ross, Topologies induced by groups of characters, Fund. Math. 55 (1964), 283-291.
7. D. N. Dikranjan, I. R. Prodanov and L. N. Stoyanov, Topological Groups. Characters, Dualities and Minimal Group Topologies, Marcel Dekker, New York, 1990.
8. I. Fleischer and T. Traynor, Continuity of homomorphisms on a Baire group, Proc. Amer. Math. Soc. 93 (1985), 367-368.
9. I. Glicksberg, Uniform boundedness for groups, Canad. J. Math. 14 (1962), 269-276.
10. E. Hewitt and K. A. Ross, Abstract Harmonic Analysis I, Grundlehren Math. Wiss. 115, Springer, 1963.
11. H. Jarchow, Locally Convex Spaces, B. G. Teubner, Stuttgart, 1981.
12. J. Ka̧kol, Note on compatible vector topologies, Proc. Amer. Math. Soc. 99 (1987), 690-692.
13. J. Ka̧kol, The Mackey-Arens theorem for non-locally convex spaces, Collect. Math. 41 (1990), 129-132.
14. J. Ka̧kol, C. Pérez-García and W. Schikhof, Cardinality and Mackey topologies of non-Archimedian Banach and Fréchet spaces, Bull. Polish Acad. Sci. Math. 44 (1996), 131-141.
15. G. Köthe, Topological Vector Spaces I, Springer, Berlin, 1969.
16. I. Labuda and Z. Lipecki, On subseries convergent series and m-quasi-bases in topological linear spaces, Manuscripta Math. 38 (1982), 87-98.
17. I. Namioka, Separate continuity and joint continuity, Pacific J. Math. 51 (1974), 515-631.
18. N. Noble, k-groups and duality, Trans. Amer. Math. Soc. 151 (1970), 551-561.
19. B. J. Pettis, On continuity and openness of homomorphisms in topological groups, Ann. of Math. 52 (1950), 293-308.
20. D. Remus and F. J. Trigos-Arrieta, Abelian groups which satisfy Pontryagin duality need not respect compactness, Proc. Amer. Math. Soc. 117 (1993), 1195-1200.
21. W. Roelcke and S. Dierolf, On the three-space problem for topological vector spaces, Collect. Math. 32 (1981), 3-25.
22. H. H. Schaefer, Topological Vector Spaces, Springer, 1971.
23. M. F. Smith, The Pontryagin duality theorem in linear spaces, Ann. of Math. 56 (1952), 248-253.
24. J. P. Troallic, Sequential criteria for equicontinuity and uniformities on topological groups, Topology Appl. 68 (1996), 83-95.
25. N. T. Varopoulos, Studies in harmonic analysis, Proc. Cambridge Philos. Soc. 60 (1964), 467-516.
26. N. Ya. Vilenkin, The theory of characters of topological Abelian groups with a given boundedness, Izv. Akad. Nauk SSSR Ser. Mat. 15 (1951), 439-462 (in Russian).
27. J. H. Webb, Sequential convergence in locally convex spaces, Proc. Cambridge Philos. Soc. 64 (1968), 341-364.