scholarly journals Fixed points of isometries on weakly compact convex sets

2003 ◽  
Vol 282 (1) ◽  
pp. 1-7 ◽  
Author(s):  
Teck-Cheong Lim ◽  
Pei-Kee Lin ◽  
C. Petalas ◽  
T. Vidalis
Keyword(s):  
Fixed Points ◽  
Convex Sets ◽  
Compact Convex ◽  
Weakly Compact

scholarly journals Some remarks on the location of fixed points

1984 ◽  
Vol 37 (3) ◽  
pp. 358-365
Author(s):  
Michael Edelstein ◽  
Daryl Tingley
Keyword(s):  
Banach Space ◽  
Fixed Points ◽  
Convex Subset ◽  
Compact Convex ◽  
Compact Convex Subset ◽  
Chebyshev Center ◽  
Weakly Compact ◽  
Asymptotic Center

AbstractSeveral procedures for locating fixed points of nonexpansive selfmaps of a weakly compact convex subset of a Banach space are presented. Some of the results involve the notion of an asymptotic center or a Chebyshev center.

On Super Weakly Compact Convex Sets and Representation of the Dual of the Normed Semigroup They Generate

2013 ◽  
Vol 56 (2) ◽  
pp. 272-282 ◽  
Author(s):  
Lixin Cheng ◽  
Zhenghua Luo ◽  
Yu Zhou
Keyword(s):  
Banach Space ◽  
Convex Sets ◽  
Convex Set ◽  
Compact Convex ◽  
Lower Semicontinuous ◽  
Weakly Compact ◽  
Bounded Set ◽  
Fréchet Differentiable ◽  
Bounded Convex

AbstractIn this note, we first give a characterization of super weakly compact convex sets of a Banach space X: a closed bounded convex set K ⊂ X is super weakly compact if and only if there exists a w* lower semicontinuous seminorm p with p ≥ σK ≌ supxєK 〈.,x〉 such that p2 is uniformly Fréchet differentiable on each bounded set of X*. Then we present a representation theoremfor the dual of the semigroup swcc(X) consisting of all the nonempty super weakly compact convex sets of the space X.

Mazur Intersection Properties for Compact and Weakly Compact Convex Sets

1998 ◽  
Vol 41 (2) ◽  
pp. 225-230 ◽  
Author(s):  
Jon Vanderwerff
Keyword(s):  
Banach Space ◽  
Convex Sets ◽  
Convex Set ◽  
Compact Convex ◽  
Weakly Compact ◽  
Compact Convex Set

AbstractVarious authors have studied when a Banach space can be renormed so that every weakly compact convex, or less restrictively every compact convex set is an intersection of balls. We first observe that each Banach space can be renormed so that every weakly compact convex set is an intersection of balls, and then we introduce and study properties that are slightly stronger than the preceding two properties respectively.

Geometric and Topological Properties of Certain w* Compact Convex sets which Arise from the Study of Invariant Means

1985 ◽  
Vol 37 (1) ◽  
pp. 107-121 ◽  
Author(s):  
Edmond E. Granirer
Keyword(s):  
Banach Space ◽  
Convex Hull ◽  
Fixed Points ◽  
Convex Sets ◽  
Compact Convex ◽  
Topological Properties ◽  
Bounded Linear ◽  
Invariant Means ◽  
Image Position ◽  
Set Of Points

Let E be a Banach space, A a subset of its dual E*.x0 ∊ A is said to be a w*Gδ point of A if there are xn ∊ E and scalars γn, n = 1,2, 3 … such thatDenote by w*Gδ{A} the set of all w*Gδ points of A. If S is a semigroup of maps on E* and K ⊂ E*, denote byi.e., the set of points x* in the w*closure of K which are fixed points of S (i.e., sx* = x* for each s in S}. An operator will mean a bounded linear map on a Banach space and Co B will denote the convex hull of B ⊂ E.

A Uniformly Asymptotically Regular Mapping Without Fixed Points

1987 ◽  
Vol 30 (4) ◽  
pp. 481-483 ◽  
Author(s):  
Pei-kee Lin
Keyword(s):  
Fixed Points ◽  
Convex Subset ◽  
Compact Convex ◽  
Compact Convex Subset ◽  
Lipschitzian Mapping ◽  
Weakly Compact ◽  
Regular Mapping ◽  
Asymptotically Regular

AbstractWe construct a uniformly asymptotically regular, Lipschitzian mapping acting on a weakly compact convex subset of l2 which has no fixed points.

scholarly journals Characterizing the metric compactification of $$L_{p}$$ spaces by random measures

2020 ◽  
Vol 11 (2) ◽  
pp. 227-243
Author(s):  
Armando W. Gutiérrez
Keyword(s):  
Fixed Points ◽  
Ergodic Theorem ◽  
Convex Subset ◽  
Polish Space ◽  
Compact Convex ◽  
Random Measure ◽  
Complete Characterization ◽  
Random Measures ◽  
Weakly Compact

AbstractWe present a complete characterization of the metric compactification of $$L_{p}$$Lp spaces for $$1\le p < \infty $$1≤p<∞. Each element of the metric compactification of $$L_{p}$$Lp is represented by a random measure on a certain Polish space. By way of illustration, we revisit the $$L_{p}$$Lp-mean ergodic theorem for $$1< p < \infty $$1<p<∞, and Alspach’s example of an isometry on a weakly compact convex subset of $$L_{1}$$L1 with no fixed points.

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