Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On the uniform ergodic theorem of Lin


Author: Stuart P. Lloyd
Journal: Proc. Amer. Math. Soc. 83 (1981), 710-714
MSC: Primary 47A35
MathSciNet review: 630042
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Lin has given necessary and sufficient conditions for convergence in the uniform operator topology of $ {A_n} = (1 + T + \cdots + {T^{n - 1}})/n$, $ T$ being a Banach space operator satisfying $ \left\Vert {{T^n}} \right\Vert/n \to 0$. We prove a generalization in which the Cesàro means are replaced by any bounded sequence in the affine hull converging uniformly to invariance. In the case where $ T:{C_0}(X) \to {C_0}(X)$ is a transient Feller operator for noncompact locally compact Hausdorff space $ X$, we show that $ \{ {A_n}\} $ converges strongly but never uniformly.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47A35

Retrieve articles in all journals with MSC: 47A35


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0630042-0
Keywords: Uniform ergodic theorem
Article copyright: © Copyright 1981 American Mathematical Society