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A functional representation of almost isometries



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Cabello, Javier and Jaramillo Aguado, Jesús Ángel (2017) A functional representation of almost isometries. Journal of Mathematical Analysis and Applications, 445 (2). pp. 1243-1257. ISSN 0022-247X

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Official URL: http://www.sciencedirect.com/science/article/pii/S0022247X16300646


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).

Item Type:Article
Uncontrolled Keywords:Almost isometries; Quasi-metric spaces; Semi-Lipschitz functions
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:40082
Deposited On:17 Nov 2016 09:18
Last Modified:18 Nov 2016 09:32

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