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
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.
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.