DW-compact operators on Banach lattices

被引：0
|
作者：
Chen, Jin Xi [1 ]
Feng, Jingge [1 ]
机构：
[1] Southwest Jiaotong Univ, Sch Math, Chengdu 610031, Peoples R China
来源：
POSITIVITY | 2025年 / 29卷 / 01期
关键词：
Disjointly weakly compact set; <italic>DW</italic>-compact operator; <italic>AM</italic>-compact operator; Almost Dunford-Pettis operator; Banach lattice; DUNFORD-PETTIS SETS;
D O I：
10.1007/s11117-024-01106-8
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This paper is devoted to the study of DW-compact operators, that is, those operators which map disjointly weakly compact sets in a Banach lattice onto relatively compact sets. We show that DW-compact operators are precisely the operators which are both Dunford-Pettis and AM-compact. As an application, Banach lattices with the property that every disjointly weakly compact set is a limited (resp. Dunford-Pettis) set, are characterized by using DW-compact operators.
引用
收藏
页数：15
相关论文
共 50 条
  • [21] The order properties of r-compact operators on Banach lattices
    Chen, Zi Li
    Wickstead, A. W.
    ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2007, 23 (03) : 457 - 466
  • [22] Order continuous extensions of positive compact operators on Banach lattices
    Chen, Jin Xi
    Chen, Zi Li
    Ji, Guo Xing
    INDAGATIONES MATHEMATICAE-NEW SERIES, 2011, 21 (3-4): : 175 - 180
  • [23] About b-weakly compact operators on Banach lattices
    Bouras, Khalid
    El Kaddouri, Abdelmonaim
    H'michane, Jawad
    Moussa, Mohammed
    RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO, 2012, 61 (03) : 355 - 360
  • [24] Positive Compact Operators on Banach Lattices: Some Loose Ends
    A.W. Wickstead
    Positivity, 2000, 4 : 313 - 325
  • [25] On the duality property for semi-compact operators on Banach lattices
    Belmesnaoui Aqzzouz
    Aziz Elbour
    Acta Scientiarum Mathematicarum, 2011, 77 (3-4): : 513 - 524
  • [26] Positive compact operators on Banach lattices: Some loose ends
    Wickstead, AW
    POSITIVITY, 2000, 4 (03) : 313 - 325
  • [27] OPERATORS ON BANACH LATTICES
    SHIELDS, PC
    NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1969, 16 (01): : 247 - &
  • [28] FACTORING COMPACT AND WEAKLY COMPACT-OPERATORS THROUGH REFLEXIVE BANACH-LATTICES
    ALIPRANTIS, CD
    BURKINSHAW, O
    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1984, 283 (01) : 369 - 381
  • [29] A note on spectral sublinearity for collections of positive compact operators on Banach lattices
    Kandic, M.
    SPECIAL MATRICES, 2018, 6 (01): : 369 - 375
  • [30] Duality properties for b-AM-compact operators on Banach lattices
    Cheng, Na
    Chen, Zi-Li
    Chen, Guang-Gui
    MATHEMATICAL NOTES, 2013, 93 (3-4) : 465 - 469
12345