International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 1, Pages 159-163

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

Copyright © 1998 Aref Kamal. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper the author studies some cases of Banach space that does not have the property P1. He shows that if X=1 or L1(μ) for some non-purely atomic measure μ, then X does not have the property P1. He also shows that if X= or C(Q) for some infinite compact Hausdorff space Q, then X* does not have the property P1.