RT Journal Article
T1 A functional representation of almost isometries
A1 Cabello, Javier
A1 Jaramillo Aguado, Jesús Ángel
AB 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).
PB Elsevier
SN 0022-247X
YR 2017
FD 2017-01-15
LK https://hdl.handle.net/20.500.14352/17553
UL https://hdl.handle.net/20.500.14352/17553
LA eng
NO Ministerio de Economía y Competitividad (MINECO)
NO Junta de Extremadura
DS Docta Complutense
RD 6 may 2024