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Acta Mathematica Sinica, English Series

, Volume 34, Issue 5, pp 873–890 | Cite as

On p-convergent Operators on Banach Lattices

  • Elroy D. Zeekoei
  • Jan H. Fourie
Article
  • 37 Downloads

Abstract

The notion of a p-convergent operator on a Banach space was originally introduced in 1993 by Castillo and Sánchez 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.

Keywords

p-convergent operator disjoint p-convergent operator weak p-convergent operator Schur property of order p positive Schur property of order p 

MR(2010) Subject Classification

47B07 47B60 46B20 

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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Unit for Business Mathematics and InformaticsNorth-West University (NWU)PotchefstroomSouth Africa

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