Biseparating maps between Lipschitz function spaces

作者：Araujo Jesus^*; Dubarbie Luis

来源：Journal of Mathematical Analysis and Applications, 2009, 357(1): 191-200.

DOI：10.1016/j.jmaa.2009.03.065

• Biseparating map
• Disjointness preserving map
• Automatic continuity
• Lipschitz function

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.

• 出版日期2009-9-1