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Strongly nuclear spaces were introduced by Martineau and Brudovskij in the sixties. It is known that the dual space of a metrizable nuclear space is not only nuclear, but even strongly nuclear. Nuclear groups were introduced in [4]. They form a class of abelian topological groups which is an analogue of the class of nuclear spaces. It was proved in [4] that the dual group of a metrizable nuclear group is a nuclear group again. In this paper we introduce strongly nuclear groups, an analogue of strongly nuclear spaces, and prove that the dual group of a metrizable nuclear group is strongly nuclear.
Wydawca
Rocznik
Tom
Strony
75--91
Opis fizyczny
Bibliogr. 19 poz.
Twórcy
autor
- Faculty of Mathematics, University of Łódź, ul. Banacha 22, 90-238 Łódź, Poland
autor
- Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain
Bibliografia
- [1] L. Auꞵenhofer, Contributions to the duality theory of abelian topological groups and to the theory of nuclear spaces, Dissertationes Math. (Rozprawy Mat.), 384 1999.
- [2] L. Auꞵenhofer, Some aspects of nuclear vector groups, Studia Math., to be published.
- [3] L. Auꞵenhofer, A survey on nuclear groups, Res. Exp. Math., 24 (2000) 1-30.
- [4] W. Banaszczyk, Additive subgroups of topological vector spaces, Lecture Notes in Math., 1466, Springer-Verlag, Berlin 1991.
- [5] W. Banaszczyk, Summable families in nuclear groups, Studia Math., 105 (1993) 271-282.
- [6] W. Banaszczyk, The Lévy continuity theorem for nuclear groups, Studia Math., 136 (1999) 183-196.
- [7] W. Banaszczyk, Theorems of Bochner and Lévy for nuclear qroups, Res. Exp. Math., 24 (2000) 31-44.
- [8] W. Banaszczyk, E. Martín-Peinador, The Glicksberg theorem on weakly compact sets for nuclear groups, Ann. New York Acad. Sci., 788 (1996) 34-39.
- [9] W. Banaszczyk, E. Martín-Peinador, Weakly pseudocompact subsets of nuclear groups, J. Pure Appl. Algebra, 138 (1999) 99-106.
- [10] W. Banaszczyk, V. Tarieladze, The strong Lévy property and related questions for nuclear groups, preprint 2000.
- [11] V. S. Brudovskiĭ, Associated nuclear topology, type s mappings and strongly nuclear spaces (in Russian), Dokl. Akad. Nauk SSSR, 178 (1968) 271-273.
- [12] V. S. Brudovskiĭ, Type s mappings of locally convex spaces (in Russian), Dokl. Akad. Nauk SSSR, 180 (1968) 15-17.
- [13] M. J. Chasco, Pontryagin duality for metrizable groups, Arch. Math. (Basel), 70 (1998) 22-28.
- [14] B. Carl, I. Stefani, Entropy, compactness and the approximation of operators, Cambridge University Press, Cambridge 1990.
- [15] J. Galindo, Structure and analysis on nuclear qroups, Houston J. Math., 26 (2000) 315-325.
- [16] A. Martineau, Sur une propriété universelle de l’espace des distributions de M. Schwartz, C. R. Acad. Sci. Paris, 259 (1964) 3162-3164.
- [17] J. Núñez García, On λ-nuclear groups, in preparation.
- [18] A. Pietsch, Nuclear locally convex spaces, Springer-Verlag, Berlin 1972.
- [19] P. Wojtaszczyk, Banach spaces for analysts, Cambridge University Press, Cambridge 1996.
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Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0001-0049