On the range of the derivative of Gâteaux-Smooth functions on separable Banach spaces

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F05%3A00025746" target="_blank" >RIV/67985840:_____/05:00025746 - 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
On the range of the derivative of Gâteaux-Smooth functions on separable Banach spaces
Original language description
We prove that there exists a Lipschitz function from l1 into R2 which is Gâteaux-differentiable at every point and such that for every x,y .. l1, the norm of f´(x) - f´(y) is bigger than 1. On the other hand, for every Lipschitz and Gâteaux-differentiable function from an arbitrary Banach space X into R and for every .. > 0, there always exist two points x,y .. X such that //f´(x)-f´(y)// is less than .. . We also construct, in every infinite dimensional separable Banach space, a real valued function fon X, which is Gâteaux-differentiable at every point, has bounded non-empty support, and with the properties that f´is norm to weak* continuous and f´(X) has an isolated point a, and that necessarily a .. 0.
Czech name
Obraz derivace Gateauovsky hladkých funkcí na separabilních Banachových prostorech
Czech description
Hlavní výsledek je příklad Lipschitzovské a Gâteauovsky hladké funkce z 1_1 do R^2 takové, že derivace v libovolných dvou různých bodech mají od sebe vzdálenost aspoň jedna.

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)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2005
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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