Disjoint Dunford-Pettis-type properties in Banach lattices

Abstract

New characterizations of the disjoint Dunford-Pettis property of order $p$ (disjoint $DP{P}_p$) are proved and applied to show that a Banach lattice of cotype $p$ has the disjoint $DP{P}_p$ whenever its dual has this property. The disjoint Dunford-Pettis${}^{\ast }$ property of order $p$ (disjoint $D{P}^{\ast }{P}_p$) is thoroughly investigated. Close connections with the positive Schur property of order $p$, with the disjoint $DP{P}_p$, with the $p$-weak $D{P}^{\ast }$ property and with the positive $D{P}^{\ast }$ property of order $p$ are established. In a final section we study the polynomial versions of the disjoint $DP{P}_p$ and of the disjoint $D{P}^{\ast }{P}_p$.

16 pages