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1992 | 102 | 3 | 257-267
Tytuł artykułu

Fréchet spaces of continuous vector-valued functions: Complementability in dual Fréchet spaces and injectivity

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Abstrakty
EN
Fréchet spaces of strongly, weakly and weak*-continuous Fréchet space valued functions are considered. Complete solutions are given to the problems of their injectivity or embeddability as complemented subspaces in dual Fréchet spaces.
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autor
  • Institute of Mathematics, A. Mickiewicz University, Matejki 48/49, 60-769 Poznań, Poland
  • Institute of Mathematics, A. Mickiewicz University, Matejki 48/49, 60-769 Poznań, Poland
Bibliografia
  • [1] S. F. Bellenot and E. Dubinsky, Fréchet spaces with nuclear Köthe quotients, Trans. Amer. Math. Soc. 273 (1982), 579-591.
  • [2] J. Bonet, M. Lindström and M. Valdivia, Two theorems of Josefson-Nissenzweig type for Fréchet spaces, preprint, 1991.
  • [3] M. Cambern and P. Greim, The bidual of C(X,E), Proc. Amer. Math. Soc. 85 (1982), 53-58.
  • [4] M. Cambern and P. Greim, The dual of a space of vector measures, Math. Z. 180 (1982), 373-378.
  • [5] M. Cambern and P. Greim, Uniqueness of preduals for spaces of continuous vector functions, Canad. Math. Bull. 31 (1988), 98-103.
  • [6] P. Cembranos, C(K,E) contains a complemented copy of $c_0$, Proc. Amer. Math. Soc. 91 (1984), 556-558.
  • [7] S. Dierolf and D. N. Zarnadze, A note on strictly regular Fréchet spaces, Arch. Math. (Basel) 42 (1984), 549-556.
  • [8] J. Diestel, Sequences and Series in Banach Spaces, Springer, New York 1984.
  • [9] P. Domański, $ℒ_p$-Spaces and injective locally convex spaces, Dissertationes Math. 298 (1990).
  • [10] P. Domański and L. Drewnowski, Uncomplementability of the spaces of norm continuous functions in some spaces of "weakly" continuous functions, Studia Math. 97 (1991), 245-251.
  • [11] P. Domański and A. Ortyński, Complemented subspaces of products of Banach spaces, Trans. Amer. Math. Soc. 316 (1989), 215-231.
  • [12] G. Emmanuele, A dual characterization of Banach spaces not containing l₁, Bull. Polish Acad. Sci. Math. 34 (1986), 155-159.
  • [13] R. Engelking, General Topology, Monograf. Mat. 60, PWN, Warszawa 1977.
  • [14] F. J. Freniche, Barrelledness of the space of vector-valued and simple functions, Math. Ann. 267 (1984), 479-486.
  • [15] H. Jarchow, Locally Convex Spaces, Birkhäuser, Stuttgart 1980.
  • [16] N. J. Kalton, Spaces of compact operators, Math. Ann. 208 (1974), 267-278.
  • [17] G. Metafune and V. B. Moscatelli, Complemented subspaces of sums and products of Banach spaces, Ann. Mat. Pura Appl. 159 (1988), 175-190.
  • [18] G. Metafune and V. B. Moscatelli, Quojections and prequojections, in: Proc. NATO-ASI Workshop on Fréchet spaces, Istanbul, August 1988, T. Terzioğlu (ed.), Kluwer, Dordrecht 1989, 235-254.
  • [19] A. Pełczyński, Some aspects of the present theory of Banach spaces, in: S. Banach, Oeuvres, Vol. II, PWN, Warszawa 1979, 218-302.
  • [20] P. Pérez Carreras and J. Bonet, Barrelled Locally Convex Spaces, North-Holland Math. Stud. 131, Elsevier/Ńorth-Holland, Amsterdam 1987.
  • [21] H. H. Schaefer, Topological Vector Spaces, Springer, Berlin 1973.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-smv102i3p257bwm
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