L1 spaces fail a certain aapproximative property

Abstract

In this paper the author studies some cases of Banach space that does not have the property P1. He shows that if X=ℓ1 or L1(μ) for some non-purely atomic measure μ, then X does not have the property P1. He also shows that if X=ℓ∞ or C(Q) for some infinite compact Hausdorff space Q, then X* does not have the property P1.