ASYMPTOTICALLY ISOMETRIC COPIES OF C(0) IN BANACH-SPACES

If Gamma is an uncountable set, then any equivalent renorming of c(0)( Gamma) contains an asymptotically isometric copy of c(0). If Y is an i nfinite dimensional closed subspace of (c(0)\\.\\infinity), then Y con tains an asymptotically isometric copy of c(0). If X and Y are two inf inite dimensional Banach spaces and if X contains an asymptotically is ometric copy of c(0), then the injective tensor product of X and Y, X (x) over cap(e)Y, contains a complemented asymptotically isometric cop y of c(0). similarly, if X contains an asymptotically isometric copy o f c(0), then the Lebesgue-Bochner space L-p([0, 1], X) contains a comp lemented asymptotically isometric copy of c(0). (C) 1998 Academic Pres s.