A note on weakly Lindelöf determined Banach spaces

A. González; Vicente Montesinos

Czechoslovak Mathematical Journal (2009)

  • Volume: 59, Issue: 3, page 613-621
  • ISSN: 0011-4642

Abstract

top
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.

How to cite

top

González, A., and Montesinos, Vicente. "A note on weakly Lindelöf determined Banach spaces." Czechoslovak Mathematical Journal 59.3 (2009): 613-621. <http://eudml.org/doc/37946>.

@article{González2009,
abstract = {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.},
author = {González, A., Montesinos, Vicente},
journal = {Czechoslovak Mathematical Journal},
keywords = {projectional generator; projectional resolution of the identity; weakly Lindelöf determined Banach space; Markushevich base; Corson compacta; projectional generator; projectional resolution of the identity; weakly Lindelöf determined Banach space; Markushevich basis; Corson compacta},
language = {eng},
number = {3},
pages = {613-621},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A note on weakly Lindelöf determined Banach spaces},
url = {http://eudml.org/doc/37946},
volume = {59},
year = {2009},
}

TY - JOUR
AU - González, A.
AU - Montesinos, Vicente
TI - A note on weakly Lindelöf determined Banach spaces
JO - Czechoslovak Mathematical Journal
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 3
SP - 613
EP - 621
AB - 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.
LA - eng
KW - projectional generator; projectional resolution of the identity; weakly Lindelöf determined Banach space; Markushevich base; Corson compacta; projectional generator; projectional resolution of the identity; weakly Lindelöf determined Banach space; Markushevich basis; Corson compacta
UR - http://eudml.org/doc/37946
ER -

References

top
  1. Amir, D., Lindenstrauss, J., 10.2307/1970554, Ann. of Math. 88 (1968), 35-44. (1968) Zbl0164.14903MR0228983DOI10.2307/1970554
  2. Fabian, M., Gateaux Differentiability of Convex Functions and Topology, Weak Asplund Spaces, John Wiley & Sons, New York (1997). (1997) Zbl0883.46011MR1461271
  3. Fabian, M., Godefroy, G., Montesinos, V., Zizler, V., 10.1016/j.jmaa.2004.02.015, J. Math. Anal. and Appl. 297 (2004), 419-455. (2004) MR2088670DOI10.1016/j.jmaa.2004.02.015
  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). (2001) MR1831176
  5. Fabian, M., Montesinos, V., Zizler, V., 10.1017/S0004972700020268, Bull. Australian Math. Soc. 65 (2002), 223-230. (2002) Zbl1007.46011MR1898536DOI10.1017/S0004972700020268
  6. Fremlin, D. H., Consequences of Martin's axioms, Cambridge University Press (1984). (1984) 
  7. Gurarii, V. I., Kadec, M. I., Minimal systems and quasicomplements in Banach spaces, Soviet Math. Dokl. 3 (1962), 966-968. (1962) 
  8. Hájek, P., Montesinos, V., Vanderwerff, J., Zizler, V., Biorthogonal Systems in Banach Spaces, CMS Books in Mathematics, Canadian Mathematical Society, Springer Verlag (2007). (2007) MR2359536
  9. Rychtář, J., 10.1017/S0004972700034298, Bull. Austr. Math. Soc. 69 (2004), 107-111. (2004) Zbl1054.46008MR2040053DOI10.1017/S0004972700034298
  10. Terenzi, P., 10.1112/jlms/s2-27.3.500, J. London Math. Soc. 27 (1983), 500-506. (1983) Zbl0488.46011MR0697142DOI10.1112/jlms/s2-27.3.500
  11. Terenzi, P., 10.1090/S0002-9947-1987-0869217-4, Trans. Amer. Math. Soc. 2 (1987), 497-511. (1987) MR0869217DOI10.1090/S0002-9947-1987-0869217-4
  12. Valdivia, M., Simultaneous resolutions of the identity operator in normed spaces, Collect. Math. 42 (1991), 265-284. (1991) Zbl0788.47024MR1203185
  13. Valdivia, M., Biorthogonal systems in certain Banach spaces, Revista Mat. Univ. Complut. Madrid 9 (1996), 191-220. (1996) Zbl0872.46007MR1435783
  14. Vanderwerff, J., 10.1007/BF02572347, Math. Z. 219 (1995), 21-30. (1995) Zbl0823.46014MR1340846DOI10.1007/BF02572347
  15. Zizler, V., Nonseparable Banach spaces, Handbook of Banach Spaces, Volume II 1143-1816, Elsevier Sci. B.V. (2003). (2003) Zbl1041.46009MR1999608

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.