Generalizations of Cesàro means and poles of the resolvent

Laura Burlando. "Generalizations of Cesàro means and poles of the resolvent." Studia Mathematica 164.3 (2004): 257-281. <http://eudml.org/doc/285299>.

@article{LauraBurlando2004,
abstract = {An improvement of the generalization-obtained in a previous article [Bu1] by the author-of the uniform ergodic theorem to poles of arbitrary order is derived. In order to answer two natural questions suggested by this result, two examples are also given. Namely, two bounded linear operators T and A are constructed such that $n^\{-2\}Tⁿ$ converges uniformly to zero, the sum of the range and the kernel of 1-T being closed, and $n^\{-3\} ∑_\{k=0\}^\{n-1\} A^\{k\}$ converges uniformly, the sum of the range of 1-A and the kernel of (1-A)² being closed. Nevertheless, 1 is a pole of the resolvent of neither T nor A.},
author = {Laura Burlando},
journal = {Studia Mathematica},
keywords = {uniform ergodic theorem; poles of the resolvent; ranges and kernels of the iterates},
language = {eng},
number = {3},
pages = {257-281},
title = {Generalizations of Cesàro means and poles of the resolvent},
url = {http://eudml.org/doc/285299},
volume = {164},
year = {2004},
}

TY - JOUR
AU - Laura Burlando
TI - Generalizations of Cesàro means and poles of the resolvent
JO - Studia Mathematica
PY - 2004
VL - 164
IS - 3
SP - 257
EP - 281
AB - An improvement of the generalization-obtained in a previous article [Bu1] by the author-of the uniform ergodic theorem to poles of arbitrary order is derived. In order to answer two natural questions suggested by this result, two examples are also given. Namely, two bounded linear operators T and A are constructed such that $n^{-2}Tⁿ$ converges uniformly to zero, the sum of the range and the kernel of 1-T being closed, and $n^{-3} ∑_{k=0}^{n-1} A^{k}$ converges uniformly, the sum of the range of 1-A and the kernel of (1-A)² being closed. Nevertheless, 1 is a pole of the resolvent of neither T nor A.
LA - eng
KW - uniform ergodic theorem; poles of the resolvent; ranges and kernels of the iterates
UR - http://eudml.org/doc/285299
ER -