wMB-PROPERTY OF ORDER p IN BANACH SPACES

Abstract

In this paper, we introduce a new property of Banach spaces called wMB-property of order p (1 ≤ p < ∞). A necessary and sufficient condition for a Banach space to have the wMB-property of order p is given. We study p-convergent operators and weakly-p-L-sets. Banach spaces with the wMB-property of order p are characterized. Also, the Dunford-Pettis property of order p and DP∗ -property of order p are studied in Banach spaces. Finally we show the relation between Pelczynski’s property (V ) and wMB-property of order p