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Noncompactness and noncompleteness in isometries of Lipschitz spaces

Abstract: We solve the following three questions concerning surjective linear isometries between spaces of Lipschitz functions Lip(X,E) and Lip(Y,F), for strictly convex normed spaces E and F and metric spaces X and Y: (i) Characterize those base spaces X and Y for which all isometries are weighted composition maps. (ii) Give a condition independent of base spaces under which all isometries are weighted composition maps. (iii) Provide the general form of an isometry, both when it is a weighted composition map and when it is not. In particular, we prove that requirements of completeness on X and Y are not necessary when E and F are not complete, which is in sharp contrast with results known in the scalar context.

 Autoría: Araujo J., Dubarbie L.,

 Fuente: Journal of Mathematical Analysis and Applications 377 (2011) 15-29

 Editorial: Academic Press Inc.

 Año de publicación: 2011

 Nº de páginas: 15

 Tipo de publicación: Artículo de Revista

 DOI: 10.1016/j.jmaa.2010.09.066

 ISSN: 0022-247X,1096-0813

 Url de la publicación: https://doi.org/10.1016/j.jmaa.2010.09.066