ON THE STRUCTURE OF LIPSCHITZ-FREE SPACES

被引：43

作者：

Cuth, Marek ^{[1
,2
]}

Doucha, Michal ^{[3
]}

Wojtaszczyk, Przemyslaw ^{[4
]}

机构：

[1] Polskiej Akad Nauk, Inst Matemat, Sniadeckich 8, PL-00656 Warsaw, Poland

[2] Charles Univ Prague, Fac Math & Phys, Dept Math Anal, Sokolovska 83, Prague 18675 8, Czech Republic

[3] Polskiej Akad Nauk, Inst Matemat, Sniadeckich 8, PL-00656 Warsaw, Poland

[4] Univ Warsaw, Interdisciplinary Ctr Math & Computat Modelling, Ul Prosta 69, PL-02838 Warsaw, Poland

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2016年 / 144卷 / 09期

关键词：

Lipschitz-free space; isomorphically universal separable Banach space; embedding of c(0);

D O I：

10.1090/proc/13019

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this note we study the structure of Lipschitz-free Banach spaces. We show that every Lipschitz-free Banach space over an infinite metric space contains a complemented copy of l(1). This result has many consequences for the structure of Lipschitz-free Banach spaces. Moreover, we give an example of a countable compact metric space K such that F(K) is not isomorphic to a subspace of L-1 and we show that whenever M is a subset of R-n, then F(M) is weakly sequentially complete; in particular, c(0) does not embed into F(M).

引用

页码：3833 / 3846

页数：14

共 50 条

[1] On the preserved extremal structure of Lipschitz-free spaces
Aliaga, Ramon J.
Guirao, Antonio J.
[J]. STUDIA MATHEMATICA, 2019, 245 (01) : 1 - 14
[2] Some remarks on the structure of Lipschitz-free spaces
Hajek, Petr
Novotny, Matej
[J]. BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN, 2017, 24 (02) : 283 - 304
[3] Lipschitz-free Banach spaces
Godefroy, G
Kalton, NJ
[J]. STUDIA MATHEMATICA, 2003, 159 (01) : 121 - 141
[4] Supports in Lipschitz-free spaces and applications to extremal structure
Aliaga, Ramon J.
Pernecka, Eva
Petitjean, Colin
Prochazka, Antonin
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2020, 489 (01)
[5] 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
[6] 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
[7] Lipschitz-Free Spaces Over Ultrametric Spaces
Cuth, Marek
Doucha, Michal
[J]. MEDITERRANEAN JOURNAL OF MATHEMATICS, 2016, 13 (04) : 1893 - 1906
[8] Lipschitz-free spaces and Schur properties
Petitjean, C.
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2017, 453 (02) : 894 - 907
[9] On Schauder bases in Lipschitz-free spaces
Hajek, Petr
Pernecka, Eva
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2014, 416 (02) : 629 - 646
[10] Lipschitz geometry of operator spaces and Lipschitz-free operator spaces
Bruno M. Braga
Javier Alejandro Chávez-Domínguez
Thomas Sinclair
[J]. Mathematische Annalen, 2024, 388 : 1053 - 1090

← 1 2 3 4 5 →