On differentiability of convex operators

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F13%3A10189658" target="_blank" >RIV/00216208:11320/13:10189658 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jmaa.2012.12.073" target="_blank" >http://dx.doi.org/10.1016/j.jmaa.2012.12.073</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jmaa.2012.12.073" target="_blank" >10.1016/j.jmaa.2012.12.073</a>

Result language
angličtina
Original language name
On differentiability of convex operators
Original language description
The main known results on differentiability of continuous convex operators f from a Banach space X to an ordered Banach space Y are due to J.M. Borwein and N.K. Kirov. Our aim is to prove some "supergeneric" results, i.e., to show that, sometimes, the set of Gateaux or Frechet nondifferentiability points is not only a first-category set, but also smaller in a stronger sense. For example, we prove that if Y is countably Daniell and the space L(X, Y) of bounded linear operators is separable, then each continuous convex operator f:X -> Y is Frechet differentiable except for a Gamma-null angle-small set. Some applications of such supergeneric results are shown.
Czech name
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Czech description
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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
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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