On uniformly differentiable mappings from l(infinity) (Gamma)

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F16%3A00242770" target="_blank" >RIV/68407700:21230/16:00242770 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jmaa.2016.02.043" target="_blank" >http://dx.doi.org/10.1016/j.jmaa.2016.02.043</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jmaa.2016.02.043" target="_blank" >10.1016/j.jmaa.2016.02.043</a>

Result language
angličtina
Original language name
On uniformly differentiable mappings from l(infinity) (Gamma)
Original language description
In 1970 Haskell Rosenthal proved that if X is a Banach space, I' is an infinite index set, and T : l(infinity)(Gamma) -- X is a bounded linear operator such that inf-yEr 11T(67)11 > 0 then T acts as an isomorphism on l(infinity)(Gamma'), for some r, C P of the same cardinality as P. Our main result is a nonlinear strengthening of this theorem. More precisely, under the assumption of GCH and the regularity of I', we show that if F : Bl(infinity)(r) X is uniformly differentiable and such that infer 11F(e-y) F(0)11 > 0 then there exists x E l(infinity)(Gamma) such that dF(x)[.] is a bounded linear operator which acts as an isomorphism on l(infinity)(Gamma), for some Gamma' C r of the same cardinality as r. (C) 2016 Published by Elsevier Inc.
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
<a href="/en/project/GA16-07378S" target="_blank" >GA16-07378S: Nonlinear analysis in Banach spaces</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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