Asymptotically isometric copies of lp (1≤p<∞) and c0 in banach spaces

Let X be a Banach space. If there exists a quotient space of X which is asymptotically isometric to l(1), then X contains complemented asymptotically isometric copies of l(1). Every infinite dimensional closed subspace of l(1), contains a complemented subspace of l(1) which is asymptotically isometric to l(1). Let X be a sepal-able Banach space such that X* contains asymptotically isometric copies of l(p) (1 < p < infinity). Then there exists a quotient space of X which is asymptotically isometric to l(q) (1/p +1/q = 1). Complemented asymptotically isometric copies of c(o) in K(X, Y) and W(X, Y) are discussed. Let X be a Gelfand-Phillips space. If X contains asymptotically isometric copies of c(o), it has to contain complemented asymptotically isometric copies of c(o).