Taiwanese Journal of Mathematics

MEAN ERGODIC THEOREMS FOR ALMOST PERIODIC SEMIGROUPS

Hiromichi Miyake and Wataru Takahashi

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Abstract

We show mean ergodic theorems for vector-valued weakly almost periodic functions (in the sense of Eberlein) defined on a semigroup which take values in a locally convex topological vector space. Next, motivated by Fréchet [10], we study the relationship between almost periodicity of semigroups of mappings and their equicontinuity, and also prove mean ergodic theorems for equicontinuous semigroups.

Article information

Source
Taiwanese J. Math., Volume 14, Number 3B (2010), 1079-1091.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500405906

Digital Object Identifier
doi:10.11650/twjm/1500405906

Mathematical Reviews number (MathSciNet)
MR2674597

Zentralblatt MATH identifier
1211.43003

Subjects
Primary: 43A60: Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions 46E40: Spaces of vector- and operator-valued functions 47H20: Semigroups of nonlinear operators [See also 37L05, 47J35, 54H15, 58D07] 47H25: Nonlinear ergodic theorems [See also 28Dxx, 37Axx, 47A35]

Keywords
weakly almost periodic functions ergodic theorem invariant mean equicontinuous mapping

Citation

Miyake, Hiromichi; Takahashi, Wataru. MEAN ERGODIC THEOREMS FOR ALMOST PERIODIC SEMIGROUPS. Taiwanese J. Math. 14 (2010), no. 3B, 1079--1091. doi:10.11650/twjm/1500405906. https://projecteuclid.org/euclid.twjm/1500405906


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