A Characterization of Weakly Lindelöf Determined Banach Spaces

Kalenda, Ondřej

Serdica Mathematical Journal (2003)

  • Volume: 29, Issue: 2, page 95-108
  • ISSN: 1310-6600

Abstract

top
2000 Mathematics Subject Classification: 46B26, 46B03, 46B04.We prove that a Banach space X is weakly Lindelöf determined if (and only if) each non-separable Banach space isomorphic to a complemented subspace of X has a projectional resolution of the identity. This answers a question posed by S. Mercourakis and S. Negrepontis and yields a converse of Amir-Lindenstrauss’ theorem. We also prove that a Banach space of the form C(K) where K is a continuous image of a Valdivia compactum is weakly Lindelöf determined if (and only if) each non-separable Banach space isometric to a subspace of C(K) has a projectional resolution of the identity.This work was partially supported by Research grants GAUK 1/1998, GAUK 160/1999, GA CR 201/00/1466 and MSM 113200007.

How to cite

top

Kalenda, Ondřej. "A Characterization of Weakly Lindelöf Determined Banach Spaces." Serdica Mathematical Journal 29.2 (2003): 95-108. <http://eudml.org/doc/219546>.

@article{Kalenda2003,
abstract = {2000 Mathematics Subject Classification: 46B26, 46B03, 46B04.We prove that a Banach space X is weakly Lindelöf determined if (and only if) each non-separable Banach space isomorphic to a complemented subspace of X has a projectional resolution of the identity. This answers a question posed by S. Mercourakis and S. Negrepontis and yields a converse of Amir-Lindenstrauss’ theorem. We also prove that a Banach space of the form C(K) where K is a continuous image of a Valdivia compactum is weakly Lindelöf determined if (and only if) each non-separable Banach space isometric to a subspace of C(K) has a projectional resolution of the identity.This work was partially supported by Research grants GAUK 1/1998, GAUK 160/1999, GA CR 201/00/1466 and MSM 113200007.},
author = {Kalenda, Ondřej},
journal = {Serdica Mathematical Journal},
keywords = {Weakly Lindelöf Determined Banach Space; Projectional Resolution of the Identity; Complemented Subspace; Corson Compact Space; Valdivia Compact Space; WLD Banach space; projectional resolution of identity},
language = {eng},
number = {2},
pages = {95-108},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {A Characterization of Weakly Lindelöf Determined Banach Spaces},
url = {http://eudml.org/doc/219546},
volume = {29},
year = {2003},
}

TY - JOUR
AU - Kalenda, Ondřej
TI - A Characterization of Weakly Lindelöf Determined Banach Spaces
JO - Serdica Mathematical Journal
PY - 2003
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 29
IS - 2
SP - 95
EP - 108
AB - 2000 Mathematics Subject Classification: 46B26, 46B03, 46B04.We prove that a Banach space X is weakly Lindelöf determined if (and only if) each non-separable Banach space isomorphic to a complemented subspace of X has a projectional resolution of the identity. This answers a question posed by S. Mercourakis and S. Negrepontis and yields a converse of Amir-Lindenstrauss’ theorem. We also prove that a Banach space of the form C(K) where K is a continuous image of a Valdivia compactum is weakly Lindelöf determined if (and only if) each non-separable Banach space isometric to a subspace of C(K) has a projectional resolution of the identity.This work was partially supported by Research grants GAUK 1/1998, GAUK 160/1999, GA CR 201/00/1466 and MSM 113200007.
LA - eng
KW - Weakly Lindelöf Determined Banach Space; Projectional Resolution of the Identity; Complemented Subspace; Corson Compact Space; Valdivia Compact Space; WLD Banach space; projectional resolution of identity
UR - http://eudml.org/doc/219546
ER -

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.