Proceedings of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Help
ISSN 1088-6826(e) ISSN 0002-9939(p)

Strong ergodic theorems for commutative semigroups of operators

Author(s): O. Kada
Journal: Proc. Amer. Math. Soc. 127 (1999), 3003-3011.
MSC (1991): Primary 47A35, 47H09, 47H20
Posted: May 4, 1999
MathSciNet review: 1636382
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: We prove strong mean convergence theorems and the existence of ergodic projection and retraction for commutative semigroups of operators which is Eberlein-weakly almost periodic.

References:

1.: J. B. Baillon, Un théorème de type ergodique pour les contractions non linéaires dans un espace de Hilbert, C. R. Acad. Sci. Paris Sér. A-B, 280 (1975), 1511-1514. MR 51:11205
2.: J. B. Baillon, Quelques propriétés de convergence asymptotique pour les semigroups de contractions impaires, C. R. Acad. Sci. Paris Sér. A-B, 283 (1976), 75-78. MR 54:13655
3.: J. F. Berglund, H. D. Junghenn and P. Milnes, Analysis on semigroups, John Wiley & Sons, 1989. MR 91b:43001
4.: R. E. Bruck, On the almost-convergence of iterates of a nonexpansive mapping in Hilbert space and the structure of the weak $\omega$ -limit set, Israel J. Math., 29 (1978), 1-16. MR 58:2474
5.: R. E. Bruck, On the convex approximation property and the asymptotic behavior of nonlinear contractions in Banach spaces, Israel J. Math., 38 (1981), 304-314. MR 82h:47051
6.: M. M. Day, Amenable semigroups, Illinois J. Math., 1 (1957), 509-544. MR 19:1067c
7.: M. M. Day, Fixed point theorem for compact convex sets, Illinois J. Math., 5 (1961), 585-590; 8 (1964), 713. MR 25:1547; MR 29:6463
8.: K. DeLeeuw and I. Glicksberg, Applications of almost periodic compactifications, Acta Math. 105 (1961), 63-97. MR 24:A1632
9.: W. F. Eberlein, Abstract ergodic theorems and weak almost periodic functions, Trans. Amer. Math. Soc. 667 (1949), 217-240. MR 12:112a
10.: S. Goldberg and P. Irwin, Weakly almost periodic vector-valued functions, Diss. Math. 157 (1979), 46pp. MR 80e:43010
11.: N. Hirano, K. Kido and W. Takahashi, Asymptotic behavior of commutative semigroups of nonexpansive mappings in Banach spaces, Nonlinear Analysis, 10 (1986), 229-249. MR 87d:47078
12.: N. Hirano, K. Kido and W. Takahashi, Nonexpansive retractions and nonlinear ergodic theorems in Banach spaces, Nonlinear Analysis, 12 (1988), 1269-1281. MR 90a:47138
13.: O. Kada, Existence of ergodic retraction for noncommutative semigroups in Banach spaces, submitted.
14.: O. Kada, Strong ergodic theorems for noncommutative semigroups in Banach spaces, preprint.
15.: O. Kada and W. Takahashi, Nonlinear ergodic theorems of almost nonexpansive curves for commutative semigroups, Topological Methods in Nonlinear Analysis, 5 (1995), 305-324. MR 97f:47053
16.: O. Kada and W. Takahashi, Strong convergence and nonlinear ergodic theorems for commutative semigroups of nonexpansive mappings, Nonlinear Analysis, 28 (1997), 495-511. MR 97j:47075
17.: J. L. Kelly and I. Namioka, Linear topological spaces, Van Nostrand, 1963. MR 29:3851
18.: K. Kido and W. Takahashi, Mean ergodic theorems for semigroups of linear operators, J. Math. Anal. Appl., 103 (1984), 387-394. MR 86g:47052
19.: G. G. Lorentz, A contribution to the theory of divergent series, Acta Math. 80 (1948), 167-190. MR 10:367e
20.: P. Milnes, On vector-valued weakly almost periodic functions, J. London Math. Soc., 22 (1980), 467-472. MR 82i:43007
21.: I. Miyadera and K. Kobayasi, On the asymptotic behavior of almost-orbits of nonlinear contraction semigroups in Banach spaces, Nonlinear Analysis, 6 (1982), 349-365. MR 84c:47064
22.: H. Oka, On the strong ergodic theorems for commutative semigroups in Banach spaces, Tokyo J. Math., 16 (1993), 385-398. MR 94j:47086
23.: S. Reich, Almost convergence and nonlinear ergodic theorems, J. Approximation Theory, 24 (1978), 269-272. MR 80b:47079
24.: G. Rodé, An ergodic theorem for semigroups of nonexpansive mappings in a Hilbert space, J. Math. Anal. Appl., 85 (1982), 172-178. MR 83k:47038
25.: B. D. Rouhani, Asymptotic behavior of almost nonexpansive sequences in a Hilbert space, J. Math. Anal. Appl. 151 (1990), 226-235. MR 92a:47065
26.: W. M. Ruess and W. H. Summers, Weak almost periodicity and the strong ergodic limit theorem for contraction semigroups, Israel J. Math., 64 (1988), 139-157. MR 90c:47118
27.: W. M. Ruess and W. H. Summers, Integration of asymptotically almost periodic functions and weak asymptotic almost periodicity, Diss. Math. 279 (1989). MR 90d:46056
28.: W. M. Ruess and W. H. Summers, Weakly almost periodic semigroups of operators, Pacific J. Math., 143 (1990), 175-193. MR 91b:47142
29.: W. M. Ruess and W. H. Summers, Ergodic theorems for semigroup of operators, Proc. Amer. Math. Soc., 114 (1992), 423-432. MR 92e:47016
30.: W. Takahashi, A nonlinear ergodic theorem for an amenable semigroup of nonexpansive mappings in a Hilbert space, Proc. Amer. Math. Soc., 81 (1981), 253-256. MR 82f:47079
31.: W. Takahashi, Nonlinear Functional Analysis (Japanese), Kindai-kagakusha, Japan, 1988.

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|