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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Convergence of almost-orbits of nonexpansive semigroups in Banach spaces


Authors: Anthony To-Ming Lau, Koji Nishiura and Wataru Takahashi
Journal: Proc. Amer. Math. Soc. 135 (2007), 3143-3150
MSC (2000): Primary 47H20; Secondary 47H09
Published electronically: June 19, 2007
MathSciNet review: 2322744
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Abstract: The purpose of this paper is to show that the study of mean ergodic theorems for almost-orbits of semigroups of nonexpansive mappings on closed convex subsets of a Banach space can be reduced to the study of orbits for semigroups of nonexpansive mappings. This provides a unified approach to various mean ergodic theorems for almost-orbits in the literature and new applications.


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Additional Information

Anthony To-Ming Lau
Affiliation: Department of Mathematical and Satistical Sciences, University of Albert, Edmonton, Alberta, Canada T6G 2G1
Email: tlau@math.ualberta.ca

Koji Nishiura
Affiliation: Department of General Education, Fukushima National College of Technology, Taira, Iwaki-shi 970-8034, Japan
Email: nishiura@fukushima-nct.ac.jp

Wataru Takahashi
Affiliation: Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152-8552, Japan
Email: wataru@is.titech.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08999-X
PII: S 0002-9939(07)08999-X
Keywords: Mean ergodic theorem, nonexpansive semigroup, almost-orbit, regular net, invariant mean
Received by editor(s): March 31, 2006
Published electronically: June 19, 2007
Additional Notes: This research was supported by NSERC grant A-7679 and by Grant-in-Aid for General Scientific Research No. 15540157, the Ministry of Education, Science, Sports and Culture, Japan
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2007 American Mathematical Society