Asymptotically Isometric Copies of c in Banach Spaces

If G is an uncountable set, then any equivalent renorming of c0 G. contains an asymptotically isometric copy of c0. If Y is an infinite dimensional closed subspace of c05?5`., then Y contains an asymptotically isometric copy of c0. If X and Y are two infinite dimensional Banach spaces and if X contains an asymptotically isometric copy of c0 , then the injective tensor product of X and Y, Xmˆ« Y, contains a complemented asymptotically isometric copy of c0. Similarly, if X contains an asymptotically isometric copy of c0 , then the Lebesgue]Bochner space L p w0, 1x, X.contains a complemented asymptotically isometric copy of c0.