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Banach格上序Dunford-Pettis算子的相关性质 被引量：1

Some properties of order Dunford-Pettis operators on Banach lattice
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摘要 在Banach格上研究了序Dunford-Pettis算子与连续线性算子之间的关系,诸如弱紧算子,Dunford-Pettis算子和AM-紧算子,得出了一些相应的结论. This paper investigates some properties of order Dunford-Pettis operators defined in the paper[ 15]on Banach Lattice. It discusses the space condition on while each boundedoperator is order Dunford-Pettis. It also discusses the weak compactness, Dunford-Pettis property and AM-compactness of order Dunford-Pettis operators, and gets some related results.
作者 黄怀香 孙文涛 陈滋利
机构地区 西南交通大学数学学院 西藏大学理学院
出处 《西南民族大学学报（自然科学版）》 CAS 2013年第1期47-50,共4页 Journal of Southwest Minzu University(Natural Science Edition)
关键词 BANACH格 Dunford-Pettis算子 AM-紧算子 序Dunford-Pettis算子 Banach lattice Duntbrd-Pettis operator AM-compact operator order Dunford-Pettis operator
分类号 O177.2 [理学—基础数学]
  • 相关文献

参考文献14

  • 1P MEYER-NIEBERG. Banach Lattices,Universitext[M].Beilin:Springer-Verlag,1991.
  • 2C D ALIPRANTIS,O BURKINSHAW. Positive Operators[R].Springer:Reprint of the 1985 original,Dordrecht,2006.
  • 3A W WICKSTEAD. Converses for the Dodds-Fremlin and Kalton-Saab theorems[J].Mathematical Proceedings of the Cambridge Philosophical Society,1996.175-179.
  • 4S ALPAY,B ALTIN. On Riesz Space with b-Property and b-Weakly Compact Operators[J].Vladikavkaz Math,2009,(02):19-26.
  • 5B AQZZOUZ,J HMICHANE. The Duality Problem for the Class of order Weakly Compact Operators[J].Glasgow Math,2009.101-108.
  • 6B AQZZOUZ,R NOUIRA,L ZRAOILA. On the Duality Problem of Positive Dunford-Pettis Operators on Banach lattices[J].Rendiconti del Circolo Matematico di Palemo,2008.287-294.
  • 7B AQZZOUZ,A ELBOUR. Some New Results on the Class of AM-Compact Operators[J].Rendiconti del Circolo Matematico di Palemo,2010.267-275.
  • 8A C ZAANEN. Riesz spaces Ⅱ[M].North-Holland Publishing Company,1983.
  • 9B AQZZOU,R NOUIRA,L ZRAOILA. The duality problem of the class of AM-compact operators on Banach lattices[J].Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques,2008.15-20.
  • 10B AQZZOUZ,A ELBOUR,ANTHONY W. Wickstead,Positive almost Dunford-Pettis operators and their duality[J].Positivity,2011.185-197.

同被引文献16

  • 1C D ALIPRANTIS, O BURKINSHAW. Positive Operators[M]. New York: Academic Press, 1985.
  • 2P MEYER-NIEBERG. Banach Lattices[M]. Berlin: Universitext, Springer-Verlag, 1991.
  • 3A W WICKSTEAD, Converses for the Dodds-Fremlin and Kalton-Saab theorems[J] Math Proc Camb Phil Soc, 1996, 120:175- 179.
  • 4A C ZAANEN. Riesz spaces II[M]. North Holland Publishing Company, 1983.
  • 5B AQZZOUZ, J HMICHANE. The Duality Problem for the Class of order Weakly Compact Operators[J]. Glasgow Math~ 2009, 51: 101-108.
  • 6B AQZZOUZ, J HMICHANE. Some New Results on Order Weakly Operators[J]. Bohemica Math, 2009, 134: 395-367.
  • 7B AQZZOUZ, R NOUIRA, L ZRAOILA. On the Duality Problem of Positive Dunfbrd-Pettis Operators on Banach lattices[J]. Rendiconti del Circolo Matematico di Palemo, 2008, 57: 287-294.
  • 8B AQZZOUZ, J HMICHANE. Complement on order weakly compact operators[J]. Mathods of Functional Analysis and Topology, 2011, 17:112-117.
  • 9B AQZZOUZ, A ELBOUR, ANTHONY W WICKSTEAD. Positive almost Dunford-Pettis operators and their duality[J]. Positivity,(15): 185-197.
  • 10B AQZZOU, R NOUIRA, L ZRAOILA. Semi-compactness of positive Dunford-Pettis operators on Banach Lattices[J]. Amer Math Soc, 2008, 136:1997-2006.

引证文献1

西南民族大学学报（自然科学版）
2013年 第1期

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