The Fixed Point Property in c0
Canadian mathematical bulletin, Tome 41 (1998) no. 4, pp. 413-422
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A closed convex subset of ${{c}_{0}}$ has the fixed point property (fpp) if every nonexpansive self mapping of it has a fixed point. All nonempty weak compact convex subsets of ${{c}_{0}}$ are known to have the fpp. We show that closed convex subsets with a nonempty interior and nonempty convex subsets which are compact in a topology slightly coarser than the weak topology may fail to have the fpp.
Llorens-Fuster, Enrique; Sims, Brailey. The Fixed Point Property in c0. Canadian mathematical bulletin, Tome 41 (1998) no. 4, pp. 413-422. doi: 10.4153/CMB-1998-055-2
@article{10_4153_CMB_1998_055_2,
author = {Llorens-Fuster, Enrique and Sims, Brailey},
title = {The {Fixed} {Point} {Property} in c0},
journal = {Canadian mathematical bulletin},
pages = {413--422},
year = {1998},
volume = {41},
number = {4},
doi = {10.4153/CMB-1998-055-2},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1998-055-2/}
}
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