Order isomorphisms on convex functions in windows

Shiri Artstein-Avidan*, Dan Florentin, Vitali Milman

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


In this paper we give a characterization of all order isomorphisms on some classes of convex functions. We deal with the class Cvx(K) consisting of lower-semi-continuous convex functions defined on a convex set K, and its subclass of non negative functions attaining the value zero at the origin. We show that any order isomorphism on these classes must be induced by a point map on the epi-graphs of the functions, and determine the exact form of this map. To this end we study convexity preserving maps on subsets of , and also in this area we have some new interpretations, and proofs.

Original languageEnglish
Title of host publicationGeometric Aspects of Functional Analysis
Subtitle of host publicationIsrael Seminar 2006-2010
PublisherSpringer Verlag
Number of pages62
ISBN (Print)9783642298486
StatePublished - 2012

Publication series

NameLecture Notes in Mathematics
ISSN (Print)0075-8434


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