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On Banach spaces that contain l1 as complemented subspace.(Spanish:Sobre los espacios de Banach que contienen a l1 como complementado).

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Cembranos, Pilar (1981) On Banach spaces that contain l1 as complemented subspace.(Spanish:Sobre los espacios de Banach que contienen a l1 como complementado). Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales de Madrid, 75 (2). pp. 510-513. ISSN 0034-0596

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Official URL: http://dmle.cindoc.csic.es/revistas/detalle.php?numero=5679



Abstract

Let E and F be two Banach spaces, and let L(E,F) [WK(E,F)] denote the space of all continuous [weakly compact] linear operators from E to F. Obviously, if F is reflexive then L(E,F)=WK(E,F). The author proves that the equality L(E,F)=WK(E,F) implies the reflexivity of F if and only if E contains l1 as a complemented subspace. In the last part of the note she investigates when the space C(T,E) of all continuous functions on the compact space T with values in the Banach space E contains l1 as a complemented subspace.


Item Type:Article
Uncontrolled Keywords:Duality and reflexivity; Banach spaces
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:22591
Deposited On:27 Aug 2013 07:06
Last Modified:13 Jun 2018 08:44

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