Quotients of continuous convex functions on nonreflexive Banach spaces

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F07%3A00004395" target="_blank" >RIV/00216208:11320/07:00004395 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Quotients of continuous convex functions on nonreflexive Banach spaces
Original language description
On each nonreflexive Banach space X there exists a positive continuous convex function f such that 1/f is not a d.c. function (i.e., a difference of two continuous convex functions). This result together with known ones implies that X is reflexive if andonly if each everywhere defined quotient of two continuous convex functions is a d.c. function. Our construction gives also a stronger version of Klee's result concerning renormings of nonreflexive spaces and non-norm-attaining functionals.
Czech name
Podíly spojitých konvexních funkcí na nereflexivních Banachových prostorech
Czech description
Na každém nereflexivním Banachově prostoru existuje kladná spojitá konvexní funkce f, pro kterou 1/f není rozdílem dvou spojitých konvexních funkcí.

Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2007
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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