A Characterization of Weakly Lindelöf Determined Banach Spaces

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 -