Communications in Mathematical Analysis

A Uniform Ergodic Theorem for Some Nörlund Means

Laura Burlando

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

We obtain a uniform ergodic theorem for the sequence $\frac1{s(n)} \sum_{k=0}^n(\varDelta s)(n-k)\,T^k$, where $\varDelta$ is the inverse of the endomorphism on the vector space of scalar sequences which maps each sequence into the sequence of its partial sums, $T$ is a bounded linear operator on a Banach space and $s$ is a divergent nondecreasing sequence of strictly positive real numbers, such that $\lim_{n\rightarrow+\infty} s(n+1)/s(n)=1$ and $\varDelta^qs\in\ell_1$ for some positive integer $q$. Indeed, we prove that if $T^{n}/s(n$) converges to zero in the uniform operator topology, then the sequence of averages above converges in the same topology if and only if $1$ is either in the resolvent set of $T$, or a simple pole of the resolvent function of $T$.

Article information

Source
Commun. Math. Anal., Volume 21, Number 2 (2018), 1-34.

Dates
First available in Project Euclid: 5 October 2018

Permanent link to this document
https://projecteuclid.org/euclid.cma/1538704836

Mathematical Reviews number (MathSciNet)
MR3866091

Zentralblatt MATH identifier
07002173

Subjects
Primary: 47A35: Ergodic theory [See also 28Dxx, 37Axx] 47A10: Spectrum, resolvent

Keywords
bounded linear operators uniform ergodic theorem Nörlund means of operator iterates spectrum poles of the resolvent concave real sequences least concave majorant of a real sequence

Citation

Burlando, Laura. A Uniform Ergodic Theorem for Some Nörlund Means. Commun. Math. Anal. 21 (2018), no. 2, 1--34. https://projecteuclid.org/euclid.cma/1538704836


Export citation