2010/06/15 by Jesús Araujo, Araujo, Jesus, Luis Dubarbie +1
Mathematics · #2010: 47B33 (Primary) #46B04 #46E15 #46E40 #47B38 (Secondary) #Advanced Banach Space Theory #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.1006.2995
openalex publication_date 2010/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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: \beginenumerate \item Characterize those base spaces X and Y for which all isometries are weighted composition maps. \item Give a condition independent of base spaces under which all isometries are weighted composition maps. \item Provide the general form of an isometry, both when it is a weighted composition map and when it is not. \endenumerate 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.