ISOMETRIES OF COMBINATORIAL BANACH SPACES

被引：11

作者：

Brech, C. ^{[1
]}

Ferenczi, V ^{[1
,2
]}

Tcaciuc, A. ^{[3
]}

机构：

[1] Univ Sao Paulo, Inst Matemat & Estat, Dept Matemat, Rua Matao 1010, BR-05508090 Sao Paulo, SP, Brazil

[2] Sorbonne Univ, UPMC, Inst Math Jussieu, Equipe Anal Fonct, Case 247,4 Pl Jussieu, F-75252 Paris 05, France

[3] MacEwan Univ, Dept Math & Stat, 10700-104 Ave, Edmonton, AB T5J 4S2, Canada

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2020年 / 148卷 / 11期

基金：

巴西圣保罗研究基金会;

关键词：

Regular families; combinatorial spaces; isometry group; Schreier families;

D O I：

10.1090/proc/15122

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that every isometry between two combinatorial spaces is determined by a permutation of the canonical unit basis combined with a change of signs. As a consequence, we show that in the case of Schreier spaces, all the isometries are given by a change of signs of the elements of the basis. Our results hold for both the real and the complex cases.

引用

页码：4845 / 4854

页数：10

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