Asymptotically isometric copies of c0 and renormings of Banach spaces

[摘要] If a Banach space X contains an asymptotically isometric copy of c(0), then X fails to have weak normal structure. Consequently, if X is an infinite-dimensional subspace of (c(0), parallel to . parallel to(infinity)), then X fails to have weak normal structure. Also, every equivalent renorming of c(0)(Gamma), for Gamma uncountable, fails to have weak normal structure. Every separable Banach space can be equivalently renormed so as not to contain an asymptotically isometric copy of c(0). Every Banach space with the generalized Gossez-Lami Dozo (GGLD) property fails to contain a subspace isomorphic to c(0). (C) 1998 Academic Press.

[发布日期] 1998-12-01

[关键词] asymptotically isometric copy of c(0);weak normal structure