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Statements

Subject Item
n2:RIV%2F00216208%3A11320%2F12%3A10127319%21RIV13-AV0-11320___
rdf:type
n6:Vysledek skos:Concept
rdfs:seeAlso
http://dx.doi.org/10.1007/s00209-011-0915-6
dcterms:description
Let X be a Hausdorff topological vector space, X * its topological dual and Z a subset of X *. In this paper, we establish some results concerning the sigma(X,Z)-approximate fixed point property for bounded, closed convex subsets C of X. Three major situations are studied. First, when Z is separable in the strong topology. Second, when X is a metrizable locally convex space and Z = X *, and third when X is not necessarily metrizable but admits a metrizable locally convex topology compatible with the duality. Our approach focuses on establishing the Frechet-Urysohn property for certain sets with regarding the sigma(X, Z)-topology. The support tools include the Brouwer's fixed point theorem and an analogous version of the classical Rosenthal's l_1-theorem for l_1-sequences in metrizable case. The results are novel and generalize previous work obtained by the authors in Banach spaces. Let X be a Hausdorff topological vector space, X * its topological dual and Z a subset of X *. In this paper, we establish some results concerning the sigma(X,Z)-approximate fixed point property for bounded, closed convex subsets C of X. Three major situations are studied. First, when Z is separable in the strong topology. Second, when X is a metrizable locally convex space and Z = X *, and third when X is not necessarily metrizable but admits a metrizable locally convex topology compatible with the duality. Our approach focuses on establishing the Frechet-Urysohn property for certain sets with regarding the sigma(X, Z)-topology. The support tools include the Brouwer's fixed point theorem and an analogous version of the classical Rosenthal's l_1-theorem for l_1-sequences in metrizable case. The results are novel and generalize previous work obtained by the authors in Banach spaces.
dcterms:title
On the approximate fixed point property in abstract spaces On the approximate fixed point property in abstract spaces
skos:prefLabel
On the approximate fixed point property in abstract spaces On the approximate fixed point property in abstract spaces
skos:notation
RIV/00216208:11320/12:10127319!RIV13-AV0-11320___
n6:predkladatel
n10:orjk%3A11320
n4:aktivita
n14:Z n14:P
n4:aktivity
P(IAA100190901), Z(MSM0021620839)
n4:cisloPeriodika
3-4
n4:dodaniDat
n15:2013
n4:domaciTvurceVysledku
n19:8577048
n4:druhVysledku
n9:J
n4:duvernostUdaju
n13:S
n4:entitaPredkladatele
n20:predkladatel
n4:idSjednocenehoVysledku
156353
n4:idVysledku
RIV/00216208:11320/12:10127319
n4:jazykVysledku
n18:eng
n4:klicovaSlova
Frechet-Urysohn space; l_1 sequence; Metrizable locally convex space; Weak approximate fixed point property
n4:klicoveSlovo
n7:l_1%20sequence n7:Weak%20approximate%20fixed%20point%20property n7:Frechet-Urysohn%20space n7:Metrizable%20locally%20convex%20space
n4:kodStatuVydavatele
DE - Spolková republika Německo
n4:kontrolniKodProRIV
[3A60EC954C37]
n4:nazevZdroje
Mathematische Zeitschrift
n4:obor
n16:BA
n4:pocetDomacichTvurcuVysledku
1
n4:pocetTvurcuVysledku
3
n4:projekt
n22:IAA100190901
n4:rokUplatneniVysledku
n15:2012
n4:svazekPeriodika
271
n4:tvurceVysledku
Lin, P-K Barroso, C. S. Kalenda, Ondřej
n4:wos
000306342700035
n4:zamer
n12:MSM0021620839
s:issn
0025-5874
s:numberOfPages
15
n3:doi
10.1007/s00209-011-0915-6
n21:organizacniJednotka
11320