Mean lower bounds for Markov operators

Eduard Emel'yanov, and Manfred Wolff. "Mean lower bounds for Markov operators." Annales Polonici Mathematici 83.1 (2004): 11-19. <http://eudml.org/doc/281018>.

@article{EduardEmelyanov2004,
abstract = {Let T be a Markov operator on an L¹-space. We study conditions under which T is mean ergodic and satisfies dim Fix(T) < ∞. Among other things we prove that the sequence $(n^\{-1\} ∑_\{k=0\}^\{n-1\} T^k)ₙ$ converges strongly to a rank-one projection if and only if there exists a function 0 ≠ h ∈ L¹₊ which satisfies $lim_\{n→∞\} ||(h - n^\{-1\} ∑_\{k=0\}^\{n-1\} T^k f)₊|| = 0$ for every density f. Analogous results for strongly continuous semigroups are given.},
author = {Eduard Emel'yanov, Manfred Wolff},
journal = {Annales Polonici Mathematici},
keywords = {Markov operator; mean ergodicity; mean lower-bound function},
language = {eng},
number = {1},
pages = {11-19},
title = {Mean lower bounds for Markov operators},
url = {http://eudml.org/doc/281018},
volume = {83},
year = {2004},
}

TY - JOUR
AU - Eduard Emel'yanov
AU - Manfred Wolff
TI - Mean lower bounds for Markov operators
JO - Annales Polonici Mathematici
PY - 2004
VL - 83
IS - 1
SP - 11
EP - 19
AB - Let T be a Markov operator on an L¹-space. We study conditions under which T is mean ergodic and satisfies dim Fix(T) < ∞. Among other things we prove that the sequence $(n^{-1} ∑_{k=0}^{n-1} T^k)ₙ$ converges strongly to a rank-one projection if and only if there exists a function 0 ≠ h ∈ L¹₊ which satisfies $lim_{n→∞} ||(h - n^{-1} ∑_{k=0}^{n-1} T^k f)₊|| = 0$ for every density f. Analogous results for strongly continuous semigroups are given.
LA - eng
KW - Markov operator; mean ergodicity; mean lower-bound function
UR - http://eudml.org/doc/281018
ER -