Group valued null sequences and metrizable non-Mackey groups

Forum Mathematicum

Volumn 26, Issue 3, 2014, Pages 723-757

  Dikranjan, Dikran ^a   Martín Peinador, Elena ^b   Tarieladze, Vaja ^c  

^a UNIVERSITY OF UDINE   (Italy)

^b UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

^c Niko Muskhelishvili Institute of Computational Mathematics   (Georgia)

Author keywords

Groups of null sequences; Locally quasi convex group; Mackey group; Mackey topology; Precompact group; Summable sequence

Indexed keywords

EID: 84902474362     PISSN: 09337741     EISSN: 14355337     Source Type: Journal    
DOI: 10.1515/forum-2011-0099     Document Type: Article

References (30)

1. H. Anzai and S. Kakutani, Bohr compactifications of a locally compact Abelian group. II, Proc. Imp. Acad. Tokyo 19 (1943), 533-539.
2. L. Aussenhofer, Contributions to the duality theory of abelian topological groups and to the theory of nuclear groups, Diss. Math. CCCLXXXIV, Warsaw, 1999.
3. L. Aussenhofer and D. de la Barrera, Linear topologies on Z are not Mackey topologies, preprint (2011), http://arxiv.org/abs/1107.2661.
4. W. Banaszczyk, Additive Subgroups of Topological Vector Spaces, Lecture Notes in Mathematics 1466, Springer-Verlag, Berlin, 1991.
5. M. Barr and H. Kleisli, On Mackey topologies in topological abelian groups, Theory Appl. Categ. 8 (2001), 54-62
6. G. Bennett and N. J. Kalton, Inclusion theorems for K-spaces, Canad. J. Math. 25 (1973), 511-524.
7. F. G. Bonales, F. J. Trigos-Arrieta and R. Vera Mendoza, A Mackey-Arens theorem for topological abelian groups, Bol. Soc. Mat. Mexicana (3) 9 (2003), no. 1, 79-88.
8. N. Bourbaki, General Topology, Volume 1, Hermann, Paris VI, 1966.
9. N. Bourbaki, General Topology, Volume 2, Hermann, Paris VI, 1966.
10. M. J. Chasco, E. Martín-Peinador and V. Tarieladze, On Mackey topology for groups, Stud. Math. 132 (1999), no. 3, 257-284.
11. W.W. Comfort and K. A. Ross, Topologies induced by groups of characters, Fund. Math. 55 (1964), 283-291.
12. W.W. Comfort and K. A. Ross, Pseudocompactness and uniform continuity in topological groups, Pacific J. Math. 16 (1966), 483-496.
13. L. De Leo, D. Dikranjan, E. Martín-Peinador and V. Tarieladze, Duality theory for groups revisited: g-barrelled, Mackey and Arens groups, preprint (2009).
14. D. Dikranjan, E. Martín-Peinador and V. Tarieladze, A class of metrizable locally quasi-convex groups which are not Mackey, preprint (2010), http://arxiv.org/abs/1012.5713.
15. D. Dikranjan, I. Prodanov and L. Stoyanov, Topological Groups: Characters, Dualities and Minimal Group Topologies, Pure and Applied Mathematics 130, Marcel Dekker, New York, 1989.
16. D. Dikranjan and D. Shakhmatov, Forcing hereditarily separable compact-like group topologies on abelian groups, Topology Appl. 151 (2005), no. 1-3, 2-54.
17. P. Enflo, Uniform structures and square roots in topological groups, Israel J. Math. 8 (1970), 230-252.
18. S. S. Gabriyelyan, Groups of quasi-invariance and the Pontryagin duality, Topology Appl. 157 (2010), no. 18, 2786-2802.
19. J. Galindo and S. Garcia-Ferreira, Compact groups containing dense pseudocompact subgroups without non-trivial convergent sequences, Topology Appl. 154 (2007), no. 2, 476-490.
20. E. Hewitt and K. A. Ross, Abstract Harmonic Analysis I, Die Grundlehren der Mathematischen Wissenschaften 115, Springer-Verlag, Berlin, 1963.
21. S. Kaplan, Extension from the Pontryagin duality I: Infinite products, Duke Math. J. 15 (1948), 649-658.
22. J. L. Kelley and I. Namioka, Linear Topological Spaces, Springer-Verlag, New York, 1963.
23. J.W. Nienhuys, A solenoidal and monothetic minimally almost periodic group, Fund. Math. 73 (1971/72), no. 2, 167-169.
24. S. Rolewicz, Some remarks on monothetic groups, Colloq. Math. XIII (1964), 28-29.
25. H. H. Schaefer, Topological Vector Spaces, The Macmillan Co., New York, Collier-Macmillan Ltd., London, 1966.
26. L. J. Sulley, On countable inductive limits of locally compact abelian groups, J. Lond. Math. Soc. (2) 5 (1972), 629-637.
27. M. Tkachenko, Self-duality in the class of precompact groups, Topology Appl. 156 (2009), no. 12, 2158-2165.
28. N. T. Varopoulos, Studies in harmonic analysis, Proc. Cambridge Philos. Soc. 60 (1964), 465-516.
29. N.Y. Vilenkin, The theory of characters of topological Abelian groups with boundedness given (in Russian), Izvestiya Akad. Nauk SSSR. Ser. Mat. 15 (1951), 439-162.
30. A. Weil, L'intégration dans les groupes topologiques et ses applications, Actualités scientifiques et industrielles 869, Hermann & Cie, Paris, 1940.