A NOTE ON NARROW OPERATORS ON COMPLEX RIESZ SPACES

被引：2
|
作者：
Popov, Mikhail [1 ,2 ]
机构：
[1] Pomeranian Univ Slupsk, Inst Exact & Tech Sci, Slupsk, Poland
[2] Vasyl Stefanyk Precarpathian Natl Univ, Ivano Frankivsk, Ukraine
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2024年 / 152卷 / 04期
关键词：
Complex Banach lattice; narrow operator; lateral order;
D O I：
10.1090/proc/16660
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The present paper continues investigation of narrow operators on complex vector lattices started in a recent paper by Dzhusoeva, Huang, Pliev and Sukochev. We answer their questions and strengthen one of their main results by proving that the extension TC: EC -+ FC of a linear operator T : E -+ F acting from a Dedekind complete real Riesz space E to a real Banach lattice F to their complexifications is narrow if and only if T is.
引用
收藏
页码：1703 / 1709
页数：7
相关论文
共 50 条
  • [1] Disjointness Preserving Operators on Complex Riesz Spaces
    J. J. Grobler
    C. B. Huijsmans
    Positivity, 1997, 1 : 155 - 164
  • [2] Disjointness preserving operators on complex Riesz spaces
    Grobler, JJ
    Huijsmans, CB
    POSITIVITY, 1997, 1 (02) : 155 - 164
  • [3] NOTE ON RIESZ OPERATORS
    CHUI, CK
    SMITH, PW
    WARD, JD
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1976, 60 (OCT) : 92 - 94
  • [4] RIESZ OPERATORS IN BANACH SPACES
    WEST, TT
    PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 1966, 16 : 131 - &
  • [5] CARLEMAN OPERATORS IN RIESZ SPACES
    GROBLER, JJ
    VANELDIK, P
    PROCEEDINGS OF THE KONINKLIJKE NEDERLANDSE AKADEMIE VAN WETENSCHAPPEN SERIES A-MATHEMATICAL SCIENCES, 1983, 86 (04): : 421 - 433
  • [6] SPACES OF OPERATORS WITH THE RIESZ SEPARATION PROPERTY
    WICKSTEAD, AW
    INDAGATIONES MATHEMATICAE-NEW SERIES, 1995, 6 (02): : 235 - 245
  • [7] NOTE ON BOCHNER-RIESZ OPERATORS
    CORDOBA, A
    DUKE MATHEMATICAL JOURNAL, 1979, 46 (03) : 505 - 511
  • [8] A note on regular martingales in Riesz spaces
    Korostenski, Mareli
    Labuschagne, Coenraad C. A.
    QUAESTIONES MATHEMATICAE, 2008, 31 (03) : 219 - 224
  • [9] HOMOMORPHISMS OF COMPLEX RIESZ SPACES
    MEYER, M
    COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1981, 292 (17): : 793 - 796
  • [10] A note on the generalized Drazin–Riesz invertible operators
    Othman Abad
    Hassane Zguitti
    Annals of Functional Analysis, 2021, 12
12345