Properties (V) and (wV) in Projective Tensor Products. (1st July 2014)

• Record Type: Journal Article
• Authors: Ghenciu, Ioana
• Other Names: Lang Jan Academic Editor.
• Is Part Of: Journal of operators. Volume 2014(2014)
• Publication Date: 2014-07-01
• Subjects: Operator theory -- Periodicals; Operator theory; Periodicals; 515.724
• DOI: 10.1155/2014/405635
• Languages: English
• ISSNs: 2314-5064

Abstract

Abstract : We give sufficient conditions for a subset ofK ( X, Y * ) = L ( X, Y * ) to be relatively weakly compact. A Banach spaceX has property( V ) (resp., ( w V ) ) if everyV -subset ofX * is relatively weakly compact (resp., weakly precompact). We prove that the projective tensor productX ⊗ π Y has property( V ) (resp., ( w V ) ), whenX has property( V ) (resp., ( w V ) ), Y has property( V ), andW ( X, Y * ) = K ( X, Y * ) .