Smooth norms and approximation in Banach spaces of the type C (K)

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F07%3A00092478" target="_blank" >RIV/67985840:_____/07:00092478 - 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
Smooth norms and approximation in Banach spaces of the type C (K)
Original language description
Two results are proved about the Banach space X = C(K), where K is compact and Hausdorff. The first concerns smooth approximation: let m be a positive integer or.INFIN.; we show that if there exists on X a non-zero function of class Cm with bounded support, then all continuous real-valued functions on X can be uniformly approximated by functions of class Cm. The second result is that if X admits a norm, equivalent to the supremum norm, with locally uniformly convex dual norm, then X also admits an equivalent norm that is of class CINFIN (except at 0).
Czech name
Hladké normy a aproximace v Banachových prostorech typu C (K)
Czech description
Pokud C(K) prostor má Ck-hladký bump, pak má též Ck-hladké rozklady jedničky. Pokud má C(K) prostor duální LUR renormaci, pak má CINFIN-hladkou normu.

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/GA201%2F04%2F0090" target="_blank" >GA201/04/0090: Geometrical analysis in Banach spaces II</a><br>
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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