STRICTLY SINGULAR OPERATORS ON BANACH LATTICES

被引：0
|
作者：
Hernandez, Francisco L. [1 ]
Semenov, Evgeny M. [2 ]
机构：
[1] Madrid Complutense Univ, IMI & Math Anal Dept, Madrid 28040, Spain
[2] Voronezh State Univ, Dept Math, Voronezh 394006, Russia
来源：
REAL ANALYSIS EXCHANGE | 2019年 / 44卷 / 01期
关键词：
Strictly singular operators; Rearrangement; invariant function spaces; Disjointly strictly singular operators; REARRANGEMENT-INVARIANT SPACES; INCLUSIONS; INTERPOLATION; IDEALS;
D O I：
10.14321/realanalexch.41.1.0037
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We survey several properties of the class of strictly singular operators defined on Banach lattices of measurable functions and rearrangement invariant function spaces. The related classes of disjointly strictly singular operators and super strictly singular operators are also discussed. In particular we present interpolation properties of strictly singular operators between L-p - L-q spaces.
引用
收藏
页码：37 / 48
页数：12
相关论文
共 50 条
  • [1] Characterizations of strictly singular operators on Banach lattices
    Flores, J.
    Hernandez, F. L.
    Kalton, N. J.
    Tradacete, P.
    JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2009, 79 : 612 - 630
  • [2] Strictly singular and power-compact operators on Banach lattices
    Julio Flores
    Francisco L. Hernández
    Evgueni M. Semenov
    Pedro Tradacete
    Israel Journal of Mathematics, 2012, 188 : 323 - 352
  • [3] STRICTLY SINGULAR AND POWER-COMPACT OPERATORS ON BANACH LATTICES
    Flores, Julio
    Hernandez, Francisco L.
    Semenov, Evgueni M.
    Tradacete, Pedro
    ISRAEL JOURNAL OF MATHEMATICS, 2012, 188 (01) : 323 - 352
  • [4] Invariant subspaces of positive strictly singular operators on Banach lattices
    Flores, Julio
    Tradacete, Pedro
    Troitsky, Vladimir G.
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 343 (02) : 743 - 751
  • [5] On strictly singular and strictly cosingular embeddings between Banach lattices of functions
    Cobos, F
    Pustylnik, E
    MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 2002, 133 : 183 - 190
  • [6] ON STRICTLY SINGULAR OPERATORS BETWEEN SEPARABLE BANACH SPACES
    Beanland, Kevin
    Dodos, Pandelis
    MATHEMATIKA, 2010, 56 (02) : 285 - 304
  • [7] STRICTLY SINGULAR OPERATORS IN ASYMPTOTIC lp BANACH SPACES
    Pelczar-Barwacz, Anna
    ILLINOIS JOURNAL OF MATHEMATICS, 2012, 56 (03) : 861 - 883
  • [8] Disjointly non-singular operators on Banach lattices
    Gonzalez, Manuel
    Martinez-Abejon, Antonio
    Martinon, Antonio
    JOURNAL OF FUNCTIONAL ANALYSIS, 2021, 280 (08)
  • [9] A class of Banach spaces with few non-strictly singular operators
    Argyros, SA
    Lopez-Abad, J
    Todorcevic, S
    JOURNAL OF FUNCTIONAL ANALYSIS, 2005, 222 (02) : 306 - 384
  • [10] STRICTLY SINGULAR AND NEARLY WEAKLY COMPACT OPERATORS IN BANACH FUNCTION SPACES
    VANELDIK, P
    GROBLER, JJ
    PROCEEDINGS OF THE KONINKLIJKE NEDERLANDSE AKADEMIE VAN WETENSCHAPPEN SERIES A-MATHEMATICAL SCIENCES, 1973, 76 (02): : 92 - 97
12345