Abstract:

Let X be a Banach space. If there exists a quotient space of X which is asymptotically isometric to l¹, then X contains complemented asymptotically isometric copies of l¹. Every infinite dimensional closed subspace of l₁ contains a complemented subspace of l₁ which is asymptotically isometric
to l₁. Let X be a separable Banach space such that X^* contains asymptotically isometric copies of l_p (1q (\frac{1}{p}+\frac{1}{q}=1). Complemented asymptotically isometric copies of c₀ in K(X,Y) and W(X,Y) are discussed. Let X be a Gelfand-Phillips space. If X contains asymptotically isometric copies of c₀, it has to contain complemented asymptotically isometric copies of c₀.

Key words: Asymptotically isometric copies of, complemented asymptoticaly isometric
copies of