Properties (V) and (wV) in Projective Tensor Products. (1st July 2014) - Ghenciu, Ioana
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 * ) .