Universidad Complutense de Madrid
E-Prints Complutense

On completion of spaces of weakly continuous functions.

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Ferrera Cuesta, Juan y Gómez Gil, Javier y Llavona, José G. (1983) On completion of spaces of weakly continuous functions. The Bulletin of the London Mathematical Society, 15 (3). 260-264 . ISSN 0024-6093

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Let E and F be two Banach spaces and let A be a nonempty subset of E . A mapping f:A→F is said to be weakly continuous if it is continuous when A has the relative weak topology and F has the topology of its norm. Let A={E} , B= {A⊂E:A is bounded} and C= {A⊂E:A is weakly compact}. Then C w (E;F) , C wb (E;F) and C wk (E;F) are the spaces of all mappings f:E→F whose restrictions to subsets A⊂E belonging to A , B and C , respectively, are weakly continuous. Clearly, C w (E;F)⊂C wb (E;F)⊂C wk (E;F) , and they are all endowed with the topology of uniform convergence on weakly compact subsets of E . The authors show that C wk (E;F) is the completion of C w (E;F) . They also show that, when E has no subspace isomorphic to l 1 , then C wb (E;F)=C wk (E;F) . When E has the Dunford-Pettis property and contains a subspace isomorphic to l 1 , the authors prove that C wb (E;F) is a proper subspace of C wk (E;F) . The same conclusion holds when E is a Banach space that contains a subspace isomorphic to l ∞ .


Tipo de documento:Artículo
Palabras clave:Topology of uniform convergence on weakly compact subsets
Materias:Ciencias > Matemáticas > Análisis matemático
Código ID:15376
Depositado:25 May 2012 08:20
Última Modificación:28 Ene 2016 15:56

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