The notion of a p-convergent operator on a Banach space was originally introduced in 1993 by Castillo and SAnehez in the paper entitled ＂Dunford-Pettis-like properties of continuous vector function spaces＂. In the p...The notion of a p-convergent operator on a Banach space was originally introduced in 1993 by Castillo and SAnehez in the paper entitled ＂Dunford-Pettis-like properties of continuous vector function spaces＂. In the present paper we consider the p-convergent operators on Banach lattices, prove some domination properties of the same and consider their applications （together with the notion of a weak p-convergent operator, which we introduce in the present paper） to a study of the Schur property of order p. Also, the notion of a disjoint p-convergent operator on Banach lattices is introduced, studied and its applications to a study of the positive Schur property of order p are considered.展开更多
基金Supported by the National Research Foundation of South Africa(Grant Nos.85619 and 101265)
文摘The notion of a p-convergent operator on a Banach space was originally introduced in 1993 by Castillo and SAnehez in the paper entitled ＂Dunford-Pettis-like properties of continuous vector function spaces＂. In the present paper we consider the p-convergent operators on Banach lattices, prove some domination properties of the same and consider their applications （together with the notion of a weak p-convergent operator, which we introduce in the present paper） to a study of the Schur property of order p. Also, the notion of a disjoint p-convergent operator on Banach lattices is introduced, studied and its applications to a study of the positive Schur property of order p are considered.
