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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.
Authorship: Araujo J., Dubarbie L.,
Fuente: Journal of Mathematical Analysis and Applications 377 (2011) 15-29
Publisher: Academic Press Inc.
Year of publication: 2011
No. of pages: 15
Publication type: Article
DOI: 10.1016/j.jmaa.2010.09.066
ISSN: 0022-247X,1096-0813
Publication Url: https://doi.org/10.1016/j.jmaa.2010.09.066
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JESUS ARAUJO GOMEZ
LUIS DUBARBIE FERNANDEZ
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