Biseparating maps between Lipschitz function spaces

被引：26

作者：

Araujo, Jesus ^{[1
]}

Dubarbie, Luis ^{[1
]}

机构：

[1] Univ Cantabria, Dept MATESCO, Fac Ciencias, E-39071 Santander, Spain

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2009年 / 357卷 / 01期

关键词：

Biseparating map; Disjointness preserving map; Automatic continuity; Lipschitz function; BANACH-STONE THEOREMS; AUTOMATIC-CONTINUITY; SEPARATING MAPS; DIFFERENTIABLE FUNCTIONS; LINEAR ISOMETRIES; ALGEBRAS; OPERATORS; REALCOMPACTNESS;

D O I：

10.1016/j.jmaa.2009.03.065

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For complete metric spaces X and Y, a description of linear biseparating maps between spaces of vector-valued Lipschitz functions defined on X and Y is provided. In particular it is proved that X and Y are bi-Lipschitz homeomorphic, and the automatic continuity of such maps is derived in some cases. Besides, these results are used to characterize the separating bijections between scalar-valued Lipschitz function spaces when Y is compact. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：191 / 200

页数：10

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