Polynomial Algebras and Smooth Functions in Banach Spaces
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F14%3A00222676" target="_blank" >RIV/68407700:21230/14:00222676 - isvavai.cz</a>
Alternative codes found
RIV/67985840:_____/14:00422561
Result on the web
<a href="http://dx.doi.org/10.1016/j.jfa.2013.11.017" target="_blank" >http://dx.doi.org/10.1016/j.jfa.2013.11.017</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jfa.2013.11.017" target="_blank" >10.1016/j.jfa.2013.11.017</a>
Alternative languages
Result language
angličtina
Original language name
Polynomial Algebras and Smooth Functions in Banach Spaces
Original language description
Let A(n)(X) be the algebra of polynomials on a real Banach space X, which is generated by all continuous polynomials of degree not exceeding n. Let m be the minimal integer such that there is a non-compact m-homogeneous polynomial P epsilon P((m) X; l(1)). Then n >= m implies that the uniform closure of A(n)(X) does not contain all polynomials of degree n + 1, and hence the chain of closures <(A(n)(X))over bar>, n >= m is strictly increasing. In the rest of the note we give solutions to three problems concerning the behaviour of smooth functions on Banach spaces posed in the literature. In particular, we construct an example of a uniformly differentiable real valued function f on the unit ball of a certain Banach space X, such that there exists no uniformly differentiable function g on lambda B-X, for any lambda > 1, which coincides with f in some neighbourhood of the origin. (C) 2013 Elsevier Inc. All rights reserved.
Czech name
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Czech description
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Classification
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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Result continuities
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)
Others
Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
JOURNAL OF FUNCTIONAL ANALYSIS
ISSN
0022-1236
e-ISSN
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Volume of the periodical
266
Issue of the periodical within the volume
3
Country of publishing house
US - UNITED STATES
Number of pages
20
Pages from-to
1627-1646
UT code for WoS article
000330253600016
EID of the result in the Scopus database
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