On Schauder bases in Lipschitz-free spaces

被引：20
|
作者：
Hajek, Petr [1 ,2 ]
Pernecka, Eva [1 ,3 ]
机构：
[1] Acad Sci Czech Republic, Math Inst, Prague 11567 1, Czech Republic
[2] Czech Tech Univ, Fac Elect Engn, Dept Math, Prague 16000 4, Czech Republic
[3] Charles Univ Prague, Fac Math & Phys, Dept Math Anal, Prague 18675 8, Czech Republic
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2014年 / 416卷 / 02期
关键词：
Lipschitz free space; Schauder basis; FREE BANACH-SPACES; APPROXIMATION PROPERTIES;
D O I：
10.1016/j.jmaa.2014.02.060
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The main result implies that the Lipschitz-free spaces F(l(1)) and F(R-n) have a Schauder basis. This improves (in a special case) on the previous work of Godefroy and Kalton who showed that F(X) has a bounded approximation property if and only if the Banach space X does. (C) 2014 Elsevier Inc. All rights reserved.
引用
收藏
页码：629 / 646
页数：18
相关论文
共 50 条
  • [1] Approximation properties and Schauder decompositions in Lipschitz-free spaces
    Lancien, G.
    Pernecka, E.
    [J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2013, 264 (10) : 2323 - 2334
  • [2] Some Remarks on Schauder Bases in Lipschitz Free Spaces
    Novotny, Matej
    [J]. BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN, 2020, 27 (01) : 111 - 126
  • [3] Schauder bases in Lipschitz free spaces over nets in Banach spaces
    Hajek, Petr
    Medina, Ruben
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2022, 512 (02)
  • [4] Schauder bases in Lipschitz free spaces over nets of L∞-spaces
    Hajek, Petr
    Medina, Ruben
    [J]. REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2023, 117 (01)
  • [5] Lipschitz-free Banach spaces
    Godefroy, G
    Kalton, NJ
    [J]. STUDIA MATHEMATICA, 2003, 159 (01) : 121 - 141
  • [6] ON THE STRUCTURE OF LIPSCHITZ-FREE SPACES
    Cuth, Marek
    Doucha, Michal
    Wojtaszczyk, Przemyslaw
    [J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2016, 144 (09) : 3833 - 3846
  • [7] Lipschitz geometry of operator spaces and Lipschitz-free operator spaces
    Braga, Bruno M.
    Chavez-Dominguez, Javier Alejandro
    Sinclair, Thomas
    [J]. MATHEMATISCHE ANNALEN, 2024, 388 (01) : 1053 - 1090
  • [8] Octahedrality in Lipschitz-free Banach spaces
    Becerra Guerrero, Julio
    Lopez-Perez, Gines
    Rueda Zoca, Abraham
    [J]. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2018, 148 (03) : 447 - 460
  • [9] Lipschitz-Free Spaces Over Ultrametric Spaces
    Cuth, Marek
    Doucha, Michal
    [J]. MEDITERRANEAN JOURNAL OF MATHEMATICS, 2016, 13 (04) : 1893 - 1906
  • [10] Lipschitz-free spaces and Schur properties
    Petitjean, C.
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2017, 453 (02) : 894 - 907
12345