Geodesic
A note on weakly Lindelöf determined Banach spaces
Czechoslovak Mathematical Journal, Tome 59 (2009) no. 3, pp. 613-621 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

We prove that weakly Lindelöf determined Banach spaces are characterized by the existence of a ``full'' projectional generator. Some other results pertaining to this class of Banach spaces are given.
We prove that weakly Lindelöf determined Banach spaces are characterized by the existence of a ``full'' projectional generator. Some other results pertaining to this class of Banach spaces are given.
Classification : 46B20, 46B26
Keywords: projectional generator; projectional resolution of the identity; weakly Lindelöf determined Banach space; Markushevich base; Corson compacta 
@article{CMJ_2009_59_3_a4,
     author = {Gonz\'alez, A. and Montesinos, V.},
     title = {A note on weakly {Lindel\"of} determined {Banach} spaces},
     journal = {Czechoslovak Mathematical Journal},
     pages = {613--621},
     year = {2009},
     volume = {59},
     number = {3},
     mrnumber = {2545644},
     zbl = {1224.46032},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2009_59_3_a4/}
}
TY  - JOUR
AU  - González, A.
AU  - Montesinos, V.
TI  - A note on weakly Lindelöf determined Banach spaces
JO  - Czechoslovak Mathematical Journal
PY  - 2009
SP  - 613
EP  - 621
VL  - 59
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/CMJ_2009_59_3_a4/
LA  - en
ID  - CMJ_2009_59_3_a4
ER  - 
%0 Journal Article
%A González, A.
%A Montesinos, V.
%T A note on weakly Lindelöf determined Banach spaces
%J Czechoslovak Mathematical Journal
%D 2009
%P 613-621
%V 59
%N 3
%U http://geodesic.mathdoc.fr/item/CMJ_2009_59_3_a4/
%G en
%F CMJ_2009_59_3_a4
González, A.; Montesinos, V. A note on weakly Lindelöf determined Banach spaces. Czechoslovak Mathematical Journal, Tome 59 (2009) no. 3, pp. 613-621. http://geodesic.mathdoc.fr/item/CMJ_2009_59_3_a4/

[1] Amir, D., Lindenstrauss, J.: The structure of weakly compact sets in Banach spaces. Ann. of Math. 88 (1968), 35-44. | DOI | MR | Zbl

[2] Fabian, M.: Gateaux Differentiability of Convex Functions and Topology. Weak Asplund Spaces, John Wiley & Sons, New York (1997). | MR | Zbl

[3] Fabian, M., Godefroy, G., Montesinos, V., Zizler, V.: Weakly compactly generated spaces and their relatives. J. Math. Anal. and Appl. 297 (2004), 419-455. | DOI | MR

[4] Fabian, M., Habala, P., Hájek, P., Pelant, J., Montesinos, V., Zizler, V.: Functional Analysis and Infinite Dimensional Geometry. Canad. Math. Soc. Books in Mathematics, 8, Springer-Verlag, New York (2001). | MR

[5] Fabian, M., Montesinos, V., Zizler, V.: Weakly compact sets and smooth norms in Banach spaces. Bull. Australian Math. Soc. 65 (2002), 223-230. | DOI | MR | Zbl

[6] Fremlin, D. H.: Consequences of Martin's axioms. Cambridge University Press (1984).

[7] Gurarii, V. I., Kadec, M. I.: Minimal systems and quasicomplements in Banach spaces. Soviet Math. Dokl. 3 (1962), 966-968.

[8] Hájek, P., Montesinos, V., Vanderwerff, J., Zizler, V.: Biorthogonal Systems in Banach Spaces. CMS Books in Mathematics, Canadian Mathematical Society, Springer Verlag (2007). | MR

[9] Rychtář, J.: On biorthogonal systems and Mazur's intersection property. Bull. Austr. Math. Soc. 69 (2004), 107-111. | DOI | MR | Zbl

[10] Terenzi, P.: Extension of uniformly minimal M-basic sequences in Banach spaces. J. London Math. Soc. 27 (1983), 500-506. | DOI | MR | Zbl

[11] Terenzi, P.: On the theory of fundamental bounded biorthogonal systems in Banach spaces. Trans. Amer. Math. Soc. 2 (1987), 497-511. | DOI | MR

[12] Valdivia, M.: Simultaneous resolutions of the identity operator in normed spaces. Collect. Math. 42 (1991), 265-284. | MR | Zbl

[13] Valdivia, M.: Biorthogonal systems in certain Banach spaces. Revista Mat. Univ. Complut. Madrid 9 (1996), 191-220. | MR | Zbl

[14] Vanderwerff, J.: Extensions of Markuševič bases. Math. Z. 219 (1995), 21-30. | DOI | MR | Zbl

[15] Zizler, V.: Nonseparable Banach spaces. Handbook of Banach Spaces, Volume II 1143-1816, Elsevier Sci. B.V. (2003). | MR | Zbl