Geodesic
A Characterization of Weakly Lindelöf Determined Banach Spaces
Serdica Mathematical Journal, Tome 29 (2003) no. 2, pp. 95-108 Cet article a éte moissonné depuis la source Bulgarian Digital Mathematics Library

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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.
Keywords: Weakly Lindelöf Determined Banach Space, Projectional Resolution of the Identity, Complemented Subspace, Corson Compact Space, Valdivia Compact Space 
@article{SMJ2_2003_29_2_a0,
     author = {Kalenda, Ond\v{r}ej},
     title = {A {Characterization} of {Weakly} {Lindel\"of} {Determined} {Banach} {Spaces}},
     journal = {Serdica Mathematical Journal},
     pages = {95--108},
     year = {2003},
     volume = {29},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SMJ2_2003_29_2_a0/}
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Kalenda, Ondřej. A Characterization of Weakly Lindelöf Determined Banach Spaces. Serdica Mathematical Journal, Tome 29 (2003) no. 2, pp. 95-108. http://geodesic.mathdoc.fr/item/SMJ2_2003_29_2_a0/