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Statements

Subject Item
n2:RIV%2F00216208%3A11320%2F13%3A10189658%21RIV14-GA0-11320___
rdf:type
n4:Vysledek skos:Concept
rdfs:seeAlso
http://dx.doi.org/10.1016/j.jmaa.2012.12.073
dcterms:description
The main known results on differentiability of continuous convex operators f from a Banach space X to an ordered Banach space Y are due to J.M. Borwein and N.K. Kirov. Our aim is to prove some %22supergeneric%22 results, i.e., to show that, sometimes, the set of Gateaux or Frechet nondifferentiability points is not only a first-category set, but also smaller in a stronger sense. For example, we prove that if Y is countably Daniell and the space L(X, Y) of bounded linear operators is separable, then each continuous convex operator f:X -> Y is Frechet differentiable except for a Gamma-null angle-small set. Some applications of such supergeneric results are shown. The main known results on differentiability of continuous convex operators f from a Banach space X to an ordered Banach space Y are due to J.M. Borwein and N.K. Kirov. Our aim is to prove some %22supergeneric%22 results, i.e., to show that, sometimes, the set of Gateaux or Frechet nondifferentiability points is not only a first-category set, but also smaller in a stronger sense. For example, we prove that if Y is countably Daniell and the space L(X, Y) of bounded linear operators is separable, then each continuous convex operator f:X -> Y is Frechet differentiable except for a Gamma-null angle-small set. Some applications of such supergeneric results are shown.
dcterms:title
On differentiability of convex operators On differentiability of convex operators
skos:prefLabel
On differentiability of convex operators On differentiability of convex operators
skos:notation
RIV/00216208:11320/13:10189658!RIV14-GA0-11320___
n4:predkladatel
n17:orjk%3A11320
n3:aktivita
n21:P
n3:aktivity
P(GA201/09/0067), P(GAP201/12/0436)
n3:cisloPeriodika
1
n3:dodaniDat
n12:2014
n3:domaciTvurceVysledku
n19:7357362
n3:druhVysledku
n20:J
n3:duvernostUdaju
n18:S
n3:entitaPredkladatele
n14:predkladatel
n3:idSjednocenehoVysledku
93689
n3:idVysledku
RIV/00216208:11320/13:10189658
n3:jazykVysledku
n5:eng
n3:klicovaSlova
Gateaux differentiability; Frechet differentiability; Convex operators; Banach lattices; Ordered normed spaces
n3:klicoveSlovo
n7:Banach%20lattices n7:Ordered%20normed%20spaces n7:Convex%20operators n7:Frechet%20differentiability n7:Gateaux%20differentiability
n3:kodStatuVydavatele
US - Spojené státy americké
n3:kontrolniKodProRIV
[38E3C75D4CCD]
n3:nazevZdroje
Journal of Mathematical Analysis and Applications
n3:obor
n16:BA
n3:pocetDomacichTvurcuVysledku
1
n3:pocetTvurcuVysledku
2
n3:projekt
n8:GA201%2F09%2F0067 n8:GAP201%2F12%2F0436
n3:rokUplatneniVysledku
n12:2013
n3:svazekPeriodika
402
n3:tvurceVysledku
Veselý, Libor Zajíček, Luděk
n3:wos
000315836900002
s:issn
0022-247X
s:numberOfPages
11
n10:doi
10.1016/j.jmaa.2012.12.073
n13:organizacniJednotka
11320