. . "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 . "231148" . . "Fr\u00E9chet-Urysohn space; l_1-sequence; Weak approximate fixed point property"@en . . "RIV/00216208:11320/11:10099051!RIV12-AV0-11320___" . "10.1016/j.jmaa.2010.06.052" . . "4"^^ . "0022-247X" . "000282196100013" . . . "[A3DE5C6EFC93]" . "1"^^ . "Spaces not containing l_1 have weak approximate fixed point property" . "1"^^ . "Journal of Mathematical Analysis and Applications" . "373" . "Kalenda, Ond\u0159ej" . "1" . "RIV/00216208:11320/11:10099051" . "P(IAA100190901), Z(MSM0021620839)" . . "11320" . . "Spaces not containing l_1 have weak approximate fixed point property"@en . . . "Spaces not containing l_1 have weak approximate fixed point property" . . . . "US - Spojen\u00E9 st\u00E1ty americk\u00E9" . . . . "Spaces not containing l_1 have weak approximate fixed point property"@en . . "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." .