A functional representation of almost isometries

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:445

Article

Cabello, Javier¹  Jaramillo, Jesus A.^2,3 

[1] Univ Extremadura, Dept Matemat, Ave Elvas S-N, Badajoz 06006, Spain

[2] Univ Complutense Madrid, IMI, E-28040 Madrid, Spain

[3] Univ Complutense Madrid, Dept Anal Matemat, Fac Ciencias Matemat, E-28040 Madrid, Spain

关键词: Almost isometries;    Quasi-metric spaces;    Semi-Lipschitz functions;   

DOI  :  10.1016/j.jmaa.2016.04.026

来源: Elsevier

【 摘 要 】

For each quasi-metric space X we consider the convex lattice SLip(1)(X) of all semi-Lipschitz functions on X with semi-Lipschitz constant not greater than 1. If X and Y are two complete quasi-metric spaces, we prove that every convex lattice isomorphism T from SLip(1)(Y) onto SLip(1)(X) can be written in the form Tf = c . (f o tau) + phi, where tau is an isometry, c > 0 and phi is an element of SLip(1)(X). As a consequence, we obtain that two complete quasi-metric spaces are almost isometric if, and only if, there exists an almost-unital convex lattice isomorphism between SLip(1)(X) and SLip(1) (Y). (C) 2016 Published by Elsevier Inc.

【 授权许可】

Free