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

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Operators with finite chain length and the ergodic theorem


Authors: K. B. Laursen and M. Mbekhta
Journal: Proc. Amer. Math. Soc. 123 (1995), 3443-3448
MSC: Primary 47A35; Secondary 46J20, 47A53, 47B06
MathSciNet review: 1277123
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: With a technical assumption (E-k), which is a relaxed version of the condition $ {T^n}/n \to 0,n \to \infty $, where T is a bounded linear operator on a Banach space, we prove a generalized uniform ergodic theorem which shows, inter alias, the equivalence of the finite chain length condition $ (X = {(I - T)^k}X \oplus \ker {(I - T)^k})$, of closedness of $ {(I - T)^k}X$, and of quasi-Fredholmness of $ I - T$. One consequence, still assuming (E-k), is that $ I - T$ is semi-Fredholm if and only if $ I - T$ is Riesz-Schauder. Other consequences are: a uniform ergodic theorem and conditions for ergodicity for certain classes of multipliers on commutative semisimple Banach algebras.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47A35, 46J20, 47A53, 47B06

Retrieve articles in all journals with MSC: 47A35, 46J20, 47A53, 47B06


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1277123-9
PII: S 0002-9939(1995)1277123-9
Article copyright: © Copyright 1995 American Mathematical Society