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

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An Entity of Type : http://linked.opendata.cz/ontology/domain/vavai/Vysledek, within Data Space : linked.opendata.cz associated with source document(s)

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
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. (cs) 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). 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). (en)
Title	Smooth norms and approximation in Banach spaces of the type C (K) Smooth norms and approximation in Banach spaces of the type C (K) (en) Hladké normy a aproximace v Banachových prostorech typu C (K) (cs)
skos:prefLabel	Smooth norms and approximation in Banach spaces of the type C (K) Smooth norms and approximation in Banach spaces of the type C (K) (en) Hladké normy a aproximace v Banachových prostorech typu C (K) (cs)
skos:notation	RIV/67985840:_____/07:00092478!RIV08-AV0-67985840
http://linked.open.../vavai/riv/strany	221;228
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GA201/04/0090), Z(AV0Z10190503)
http://linked.open...iv/cisloPeriodika	2
http://linked.open...vai/riv/dodaniDat	2008
http://linked.open...aciTvurceVysledku	Hájek, Petr
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Matematický ústav AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	450550
http://linked.open...ai/riv/idVysledku	RIV/67985840:_____/07:00092478
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	C(K) space; partitions of unity (en)
http://linked.open.../riv/klicoveSlovo	C(K) space partitions of unity
http://linked.open...odStatuVydavatele	GB - Spojené království Velké Británie a Severního Irska
http://linked.open...ontrolniKodProRIV	[0A27836CE324]
http://linked.open...i/riv/nazevZdroje	Quarterly Journal of Mathematics
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Geometrical analysis in Banach spaces II
http://linked.open...UplatneniVysledku	2007
http://linked.open...v/svazekPeriodika	58
http://linked.open...iv/tvurceVysledku	Hájek, Petr Pavel Haydon, R.
http://linked.open...n/vavai/riv/zamer	Rozvoj a prohloubení obecných matematických poznatků a jejich užití v dalších vědních oborech a v praxi
issn	0033-5606
number of pages	8 (xsd:int)
is http://linked.open...avai/riv/vysledek of	Smooth norms and approximation in Banach spaces of the type C (K) Smooth norms and approximation in Banach spaces of the type C (K) Smooth norms and approximation in Banach spaces of the type C (K)

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