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Disjoint Dunford–Pettis-Type Properties in Banach Lattices
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ABSTRACT
New characterizations of the disjoint Dunford–Pettis property of order p (disjoint DPPp) are proved and applied to show that a Banach lattice of cotype p has the disjoint DPPp whenever its dual has this property. The disjoint Dunford–Pettis$^*$ property of order p (disjoint $DP^*P_p$) is thoroughly investigated. Close connections with the positive Schur property of order p, with the disjoint DPPp, with the p-weak $DP^*$ property and with the positive $DP^*$ property of order p are established. In a final section, we study the polynomial versions of the disjoint DPPp and of the disjoint $DP^*P_p$.
Oxford University Press (OUP)
Title: Disjoint Dunford–Pettis-Type Properties in Banach Lattices
Description:
ABSTRACT
New characterizations of the disjoint Dunford–Pettis property of order p (disjoint DPPp) are proved and applied to show that a Banach lattice of cotype p has the disjoint DPPp whenever its dual has this property.
The disjoint Dunford–Pettis$^*$ property of order p (disjoint $DP^*P_p$) is thoroughly investigated.
Close connections with the positive Schur property of order p, with the disjoint DPPp, with the p-weak $DP^*$ property and with the positive $DP^*$ property of order p are established.
In a final section, we study the polynomial versions of the disjoint DPPp and of the disjoint $DP^*P_p$.
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