TY - CHAP

T1 - Order isomorphisms on convex functions in windows

AU - Artstein-Avidan, Shiri

AU - Florentin, Dan

AU - Milman, Vitali

N1 - Funding Information:
The authors would like to thank Leonid Polterovich for helpful references and comments. They also wish to thank the anonymous referee for useful remarks. Supported in part by Israel Science Foundation: first and second named authors by grant No. 865/07, second and third named authors by grant No. 491/04. All authors were partially supported by BSF grant No. 2006079.

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84865338389&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-29849-3_4

DO - 10.1007/978-3-642-29849-3_4

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AN - SCOPUS:84865338389

SN - 9783642298486

T3 - Lecture Notes in Mathematics

SP - 61

EP - 122

BT - Geometric Aspects of Functional Analysis

PB - Springer Verlag

ER -