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  • A nonempty closed convex bounded subset C of a Banach space is said to have the weak approximate fixed point property if for every continuous map f there is a sequence {x_n} in C such that x_n, f(x_n) converge weakly to 0. We prove in particular that C has this property whenever it contains no sequence equivalent to the standard basis of l_1. As a byproduct we obtain a characterization of Banach spaces not containing l_1 in terms of the weak topology.
  • A nonempty closed convex bounded subset C of a Banach space is said to have the weak approximate fixed point property if for every continuous map f there is a sequence {x_n} in C such that x_n, f(x_n) converge weakly to 0. We prove in particular that C has this property whenever it contains no sequence equivalent to the standard basis of l_1. As a byproduct we obtain a characterization of Banach spaces not containing l_1 in terms of the weak topology. (en)
Title
  • Spaces not containing l_1 have weak approximate fixed point property
  • Spaces not containing l_1 have weak approximate fixed point property (en)
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  • Spaces not containing l_1 have weak approximate fixed point property
  • Spaces not containing l_1 have weak approximate fixed point property (en)
skos:notation
  • RIV/00216208:11320/11:10099051!RIV12-AV0-11320___
http://linked.open...avai/predkladatel
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  • P(IAA100190901), Z(MSM0021620839)
http://linked.open...iv/cisloPeriodika
  • 1
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  • 231148
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  • RIV/00216208:11320/11:10099051
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  • Fréchet-Urysohn space; l_1-sequence; Weak approximate fixed point property (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • US - Spojené státy americké
http://linked.open...ontrolniKodProRIV
  • [A3DE5C6EFC93]
http://linked.open...i/riv/nazevZdroje
  • Journal of Mathematical Analysis and Applications
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  • 373
http://linked.open...iv/tvurceVysledku
  • Kalenda, Ondřej
http://linked.open...ain/vavai/riv/wos
  • 000282196100013
http://linked.open...n/vavai/riv/zamer
issn
  • 0022-247X
number of pages
http://bibframe.org/vocab/doi
  • 10.1016/j.jmaa.2010.06.052
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  • 11320
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