Biseparating maps between Lipschitz function spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:357

Article

Araujo, Jesus¹  Dubarbie, Luis¹ 

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

关键词: Biseparating map;    Disjointness preserving map;    Automatic continuity;    Lipschitz function;   

DOI  :  10.1016/j.jmaa.2009.03.065

来源: Elsevier

【 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.

【 授权许可】

Free