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

P. Domański; L. Drewnowski

Studia Mathematica (1992)

  • Volume: 102, Issue: 3, page 257-267
  • ISSN: 0039-3223

Abstract

top
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.

How to cite

top

Domański, P., and Drewnowski, L.. "Fréchet spaces of continuous vector-valued functions: Complementability in dual Fréchet spaces and injectivity." Studia Mathematica 102.3 (1992): 257-267. <http://eudml.org/doc/215927>.

@article{Domański1992,
abstract = {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.},
author = {Domański, P., Drewnowski, L.},
journal = {Studia Mathematica},
keywords = {Fréchet spaces of (weakly, weak*) continuous vector-valued functions injective Fréchet spaces; spaces complemented in dual Fréchet spaces; complemented copies of $c_0$; Josefson-Nissenzweig theorem; complemented copies of ; Fréchet spaces of strongly, weakly and weak*-continuous Fréchet space valued functions; injectivity; embeddability; complemented subspaces in dual Fréchet spaces},
language = {eng},
number = {3},
pages = {257-267},
title = {Fréchet spaces of continuous vector-valued functions: Complementability in dual Fréchet spaces and injectivity},
url = {http://eudml.org/doc/215927},
volume = {102},
year = {1992},
}

TY - JOUR
AU - Domański, P.
AU - Drewnowski, L.
TI - Fréchet spaces of continuous vector-valued functions: Complementability in dual Fréchet spaces and injectivity
JO - Studia Mathematica
PY - 1992
VL - 102
IS - 3
SP - 257
EP - 267
AB - 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.
LA - eng
KW - Fréchet spaces of (weakly, weak*) continuous vector-valued functions injective Fréchet spaces; spaces complemented in dual Fréchet spaces; complemented copies of $c_0$; Josefson-Nissenzweig theorem; complemented copies of ; Fréchet spaces of strongly, weakly and weak*-continuous Fréchet space valued functions; injectivity; embeddability; complemented subspaces in dual Fréchet spaces
UR - http://eudml.org/doc/215927
ER -

References

top
  1. [1] S. F. Bellenot and E. Dubinsky, Fréchet spaces with nuclear Köthe quotients, Trans. Amer. Math. Soc. 273 (1982), 579-591. Zbl0494.46001
  2. [2] J. Bonet, M. Lindström and M. Valdivia, Two theorems of Josefson-Nissenzweig type for Fréchet spaces, preprint, 1991. Zbl0785.46002
  3. [3] M. Cambern and P. Greim, The bidual of C(X,E), Proc. Amer. Math. Soc. 85 (1982), 53-58. Zbl0487.46017
  4. [4] M. Cambern and P. Greim, The dual of a space of vector measures, Math. Z. 180 (1982), 373-378. Zbl0471.46016
  5. [5] M. Cambern and P. Greim, Uniqueness of preduals for spaces of continuous vector functions, Canad. Math. Bull. 31 (1988), 98-103. Zbl0683.46023
  6. [6] P. Cembranos, C(K,E) contains a complemented copy of c 0 , Proc. Amer. Math. Soc. 91 (1984), 556-558. 
  7. [7] S. Dierolf and D. N. Zarnadze, A note on strictly regular Fréchet spaces, Arch. Math. (Basel) 42 (1984), 549-556. Zbl0525.46004
  8. [8] J. Diestel, Sequences and Series in Banach Spaces, Springer, New York 1984. 
  9. [9] P. Domański, p -Spaces and injective locally convex spaces, Dissertationes Math. 298 (1990). 
  10. [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. Zbl0736.46026
  11. [11] P. Domański and A. Ortyński, Complemented subspaces of products of Banach spaces, Trans. Amer. Math. Soc. 316 (1989), 215-231. Zbl0693.46017
  12. [12] G. Emmanuele, A dual characterization of Banach spaces not containing l₁, Bull. Polish Acad. Sci. Math. 34 (1986), 155-159. Zbl0625.46026
  13. [13] R. Engelking, General Topology, Monograf. Mat. 60, PWN, Warszawa 1977. 
  14. [14] F. J. Freniche, Barrelledness of the space of vector-valued and simple functions, Math. Ann. 267 (1984), 479-486. Zbl0525.46022
  15. [15] H. Jarchow, Locally Convex Spaces, Birkhäuser, Stuttgart 1980. 
  16. [16] N. J. Kalton, Spaces of compact operators, Math. Ann. 208 (1974), 267-278. Zbl0266.47038
  17. [17] G. Metafune and V. B. Moscatelli, Complemented subspaces of sums and products of Banach spaces, Ann. Mat. Pura Appl. 159 (1988), 175-190. Zbl0684.46026
  18. [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. [19] A. Pełczyński, Some aspects of the present theory of Banach spaces, in: S. Banach, Oeuvres, Vol. II, PWN, Warszawa 1979, 218-302. 
  20. [20] P. Pérez Carreras and J. Bonet, Barrelled Locally Convex Spaces, North-Holland Math. Stud. 131, Elsevier/Ńorth-Holland, Amsterdam 1987. Zbl0614.46001
  21. [21] H. H. Schaefer, Topological Vector Spaces, Springer, Berlin 1973. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.