A condition equivalent to uniform ergodicity

Maria Elena Becker. "A condition equivalent to uniform ergodicity." Studia Mathematica 167.3 (2005): 215-218. <http://eudml.org/doc/284579>.

@article{MariaElenaBecker2005,
abstract = {Let T be a linear operator on a Banach space X with $supₙ ||Tⁿ/n^\{w\}|| < ∞ $ for some 0 ≤ w < 1. We show that the following conditions are equivalent: (i) $n^\{-1\} ∑_\{k=0\}^\{n-1\} T^\{k\}$ converges uniformly; (ii) $cl(I -T)X = \{z ∈ X : lim_\{n\} ∑_\{k=1\}^\{n\} T^\{k\}z/k exists\}$.},
author = {Maria Elena Becker},
journal = {Studia Mathematica},
keywords = {uniform ergodicity; power boundedness},
language = {eng},
number = {3},
pages = {215-218},
title = {A condition equivalent to uniform ergodicity},
url = {http://eudml.org/doc/284579},
volume = {167},
year = {2005},
}

TY - JOUR
AU - Maria Elena Becker
TI - A condition equivalent to uniform ergodicity
JO - Studia Mathematica
PY - 2005
VL - 167
IS - 3
SP - 215
EP - 218
AB - Let T be a linear operator on a Banach space X with $supₙ ||Tⁿ/n^{w}|| < ∞ $ for some 0 ≤ w < 1. We show that the following conditions are equivalent: (i) $n^{-1} ∑_{k=0}^{n-1} T^{k}$ converges uniformly; (ii) $cl(I -T)X = {z ∈ X : lim_{n} ∑_{k=1}^{n} T^{k}z/k exists}$.
LA - eng
KW - uniform ergodicity; power boundedness
UR - http://eudml.org/doc/284579
ER -