Abstract :
If X is a separable Banach space, then X∗ contains an asymptotically isometric copy of l1 if and
only if there exists a quotient space of X which is asymptotically isometric to c0. If X is an infinitedimensional
normed linear space and Y is any Banach space containing an asymptotically isometric
copy of c0, then L(X,Y) contains an isometric copy of l∞. If X and Y are two infinite-dimensional
Banach spaces and Y contains an asymptotically isometric copy of c0, then Kw∗(X∗,Y) contains a
complemented asymptotically isometric copy of c0.
2003 Elsevier Inc. All rights reserved.
