International Journal of Mathematics and Mathematical Sciences 
Volume 21 (1998), Issue 1, Pages 159-163
doi:10.1155/S0161171298000210

L1 spaces fail a certain aapproximative property

Aref Kamal

 Department of Mathematics and Computer Sciences, U.A.E University, P.O Box 17551, Al-Ain, United Arab Emirates
Received 4 May 1994

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.