ABSTRACT
YUNAN CUI* Department of Mathematics, Harbin University of Science and Technology, HARBIN, 150080, P. R. China HENRYK HUDZIKf Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Matejki 48/49, 60-769 Poznan, Poland and Institute of Mathematics, Poznan University of Technology, Piotrowo 3a, 60-965 Poznan, Poland YANHONG LI Department of Mathematics, Wuhan University of Technology, Beijing, 100024, R R. China
1 INTRODUCTION
Throughout this paper X is a Banach space without the Schur property, i.e. X has a weakly convergent sequence that is not norm convergent. S(X) and B(X) denote the unit sphere and the unit ball of X , respectively and 1° denote the set of all real sequences.
