Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
It is proved that a separable Fréchet space is quasinormable if, and only if, every quotient space satisfies the density condition of Heinrich. This answers positively a conjecture of Bonet and Dí az in the class of separable Fréchet spaces.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
131-141
Opis fizyczny
Daty
wydano
1997
otrzymano
1996-07-15
poprawiono
1997-02-03
Twórcy
autor
- Dipartimento di Matematica, Università di Lecce, C.P. 193, Via per Arnesano, 73100 Lecce, Italy
Bibliografia
- [1] A. Aytuna, P. B. Djakov, A. P. Goncharov, T. Terzioğlu and V. P. Zahariuta, Some open problems in the theory of locally convex spaces, in: Linear Topological Spaces and Locally Complex Analysis I, A. Aytuna (ed.), Metu-Tübitak, Ankara, 1994, 147-164.
- [2] S. F. Bellenot, Basic sequences in non-Schwartz Fréchet spaces, Trans. Amer. Math. Soc. 258 (1980), 199-216.
- [3] S. F. Bellenot and E. Dubinsky, Fréchet spaces with nuclear Köthe quotients, ibid. 273 (1982), 579-594.
- [4] K. D. Bierstedt and J. Bonet, Stefan Heinrich's density condition for Fréchet spaces and the characterization of distinguished Köthe echelon spaces, Math. Nachr. 135 (1988), 149-180.
- [5] J. Bonet, A question of Valdivia on quasinormable Fréchet spaces, Canad. Math. Bull. 34 (1991), 301-304.
- [6] J. Bonet and J. C. Díaz, Distinguished subspaces and quotients of Köthe echelon spaces, Bull. Polish Acad. Sci. Math. 39 (1991), 177-183.
- [7] J. Bonet and J. C. Díaz, The density condition in subspaces and quotients of Fréchet spaces, Monatsh. Math. 117 (1994), 199-212.
- [8] J. C. Díaz and C. Fernández, Quotients of Köthe sequence spaces of infinite order, Arch. Math. (Basel) 66 (1996), 207-213.
- [9] A. Grothendieck, Sur les espaces (F) and (DF), Summa Brasil. Math. 3 (1954), 57-123.
- [10] S. Heinrich, Ultrapowers of locally convex spaces and applications I, Math. Nachr. 118 (1984), 211-219.
- [11] H. Jarchow, Locally Convex Spaces, Teubner, Stuttgart, 1981.
- [12] G. Köthe, Topological Vector Spaces I, II, Springer, Berlin, 1969 and 1979.
- [13] R. Meise and D. Vogt, A characterization of the quasi-normable Fréchet spaces, Math. Nachr. 122 (1985), 141-150.
Typ dokumentu
Bibliografia
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