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Statements

Subject Item
n2:RIV%2F00216208%3A11320%2F07%3A00004395%21RIV08-MSM-11320___
rdf:type
skos:Concept n19:Vysledek
dcterms:description
On each nonreflexive Banach space X there exists a positive continuous convex function f such that 1/f is not a d.c. function (i.e., a difference of two continuous convex functions). This result together with known ones implies that X is reflexive if and only if each everywhere defined quotient of two continuous convex functions is a d.c. function. Our construction gives also a stronger version of Klee's result concerning renormings of nonreflexive spaces and non-norm-attaining functionals. On each nonreflexive Banach space X there exists a positive continuous convex function f such that 1/f is not a d.c. function (i.e., a difference of two continuous convex functions). This result together with known ones implies that X is reflexive if and only if each everywhere defined quotient of two continuous convex functions is a d.c. function. Our construction gives also a stronger version of Klee's result concerning renormings of nonreflexive spaces and non-norm-attaining functionals. Na každém nereflexivním Banachově prostoru existuje kladná spojitá konvexní funkce f, pro kterou 1/f není rozdílem dvou spojitých konvexních funkcí.
dcterms:title
Quotients of continuous convex functions on nonreflexive Banach spaces Podíly spojitých konvexních funkcí na nereflexivních Banachových prostorech Quotients of continuous convex functions on nonreflexive Banach spaces
skos:prefLabel
Podíly spojitých konvexních funkcí na nereflexivních Banachových prostorech Quotients of continuous convex functions on nonreflexive Banach spaces Quotients of continuous convex functions on nonreflexive Banach spaces
skos:notation
RIV/00216208:11320/07:00004395!RIV08-MSM-11320___
n3:strany
211;217
n3:aktivita
n6:Z n6:P
n3:aktivity
P(GA201/06/0018), P(GA201/06/0198), Z(MSM0021620839)
n3:cisloPeriodika
3
n3:dodaniDat
n13:2008
n3:domaciTvurceVysledku
n7:9563245 n7:7357362 n7:8577048
n3:druhVysledku
n16:J
n3:duvernostUdaju
n18:S
n3:entitaPredkladatele
n8:predkladatel
n3:idSjednocenehoVysledku
446223
n3:idVysledku
RIV/00216208:11320/07:00004395
n3:jazykVysledku
n15:eng
n3:klicovaSlova
Quotients; continuous; convex; functions; nonreflexive; Banach; spaces
n3:klicoveSlovo
n10:Quotients n10:spaces n10:convex n10:functions n10:nonreflexive n10:continuous n10:Banach
n3:kodStatuVydavatele
PL - Polská republika
n3:kontrolniKodProRIV
[02C4396E44B0]
n3:nazevZdroje
Bulletin of the Polish Academy of Sciences - Mathematics
n3:obor
n17:BA
n3:pocetDomacichTvurcuVysledku
3
n3:pocetTvurcuVysledku
4
n3:projekt
n14:GA201%2F06%2F0018 n14:GA201%2F06%2F0198
n3:rokUplatneniVysledku
n13:2007
n3:svazekPeriodika
55
n3:tvurceVysledku
Holický, Petr Zajíček, Luděk Kalenda, Ondřej
n3:zamer
n4:MSM0021620839
s:issn
1732-8985
s:numberOfPages
7
n12:organizacniJednotka
11320