ITES2001 Fourth Italian-Spanish conference on General Topology and its applications Bressanone, 27-30 June 2001

A Banach-Stone Theorem for Lipschitz Functions

Isabel Garrido Universidad de Extremadura, Spain

Recently, we have proved that the vector lattice structure of Lip(X), the family of all real Lipschitz functions on the complete metric space X, determines the Lipschitz structure of X. Easy examples show that, in general, there is no analogous result for Lip^{∗}(X), the family of all bounded real Lipschitz functions on X. In this talk we show that a Banach-Stone type theorem for Lip^{∗}(X) works in the class of complete ”lenght spaces” or, more generally, complete quasi-convex spaces.

(Joint work with J. A. Jaramillo)