On Banach Spaces without the Approximation Property †

  • O I Reinov
  • Published 2002
1. If X is a Banach space of type p and of cotype q, then every its n-dimensional subspace is Cn 1/p−1/q-complemented in X (cf. [1]). Szankowski [2] has showed that if T (X) = sup{p : X of type p} = 2 or C(X) = inf{q : X of cotype q} = 2, then X has a subspace without the approximation property. Thus, if each subspace of X possesses the approximation… CONTINUE READING