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Dynamics of non-expansive maps on strictly convex Banach spaces
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Lemmens, Bas and van Gaans, Onno (2009) Dynamics of non-expansive maps on strictly convex Banach spaces. Israel Journal of Mathematics, Vol.171 (No.1). pp. 425-442. doi:10.1007/s11856-009-0057-2 ISSN 0021-2172.
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Official URL: http://dx.doi.org/10.1007/s11856-009-0057-2
Abstract
This paper concerns the dynamics of non-expansive maps on strictly convex finite dimensional normed spaces. By using results of Edelstein and Lyubich, we show that if X = (a"e (n) , ayen center dot ayen) is strictly convex and X has no 1-complemented Euclidean plane, then every bounded orbit of a non-expansive map f: X -> X, converges to a periodic orbit. By putting extra assumptions on the derivatives of the norm, we also show that the period of each periodic point of a non-expansive map f: X -> X is the order, or, twice the order of a permutation on n letters. This last result generalizes a theorem of Sine, who proved it for a"" (p) (n) where 1 < p < a and p not equal 2. To obtain the results we analyze the ranges of non-expansive projections, the geometry of 1-complemented subspaces, and linear isometries on 1-complemented subspaces.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Israel Journal of Mathematics | ||||
Publisher: | Magnes Press | ||||
ISSN: | 0021-2172 | ||||
Official Date: | June 2009 | ||||
Dates: |
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Volume: | Vol.171 | ||||
Number: | No.1 | ||||
Number of Pages: | 18 | ||||
Page Range: | pp. 425-442 | ||||
DOI: | 10.1007/s11856-009-0057-2 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Funder: | Marie Curie Intra European Fellowship, Netherlands Organisation for Scientific Research | ||||
Grant number: | MEIF-CT-2005-515391, 639.032.510 |
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