Geodesic
On the uniform ergodic theorem in Banach spaces that do not contain duals
Studia Mathematica, Tome 121 (1996) no. 1, pp. 67-85

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Let T be a power-bounded linear operator in a real Banach space X. We study the equality (*) $(I-T)X = {z ∈ X: sup_{n} ∥∑_{k=0}^{n} T^{k}z∥ ∞}$. For X separable, we show that if T satisfies and is not uniformly ergodic, then $\overline{(I-T)X}$ contains an isomorphic copy of an infinite-dimensional dual Banach space. Consequently, if X is separable and does not contain isomorphic copies of infinite-dimensional dual Banach spaces, then (*) is equivalent to uniform ergodicity. As an application, sufficient conditions for uniform ergodicity of irreducible Markov chains on the (positive) integers are obtained.
DOI : 10.4064/sm-121-1-67-85

Vladimir Fonf 1 ; Michael Lin 1 ; Alexander Rubinov 1

1 
@article{10_4064_sm_121_1_67_85,
     author = {Vladimir Fonf and Michael Lin and Alexander Rubinov},
     title = {On the uniform ergodic theorem in {Banach} spaces that do not contain duals},
     journal = {Studia Mathematica},
     pages = {67--85},
     publisher = {mathdoc},
     volume = {121},
     number = {1},
     year = {1996},
     doi = {10.4064/sm-121-1-67-85},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-121-1-67-85/}
}
TY  - JOUR
AU  - Vladimir Fonf
AU  - Michael Lin
AU  - Alexander Rubinov
TI  - On the uniform ergodic theorem in Banach spaces that do not contain duals
JO  - Studia Mathematica
PY  - 1996
SP  - 67
EP  - 85
VL  - 121
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/sm-121-1-67-85/
DO  - 10.4064/sm-121-1-67-85
LA  - en
ID  - 10_4064_sm_121_1_67_85
ER  - 
%0 Journal Article
%A Vladimir Fonf
%A Michael Lin
%A Alexander Rubinov
%T On the uniform ergodic theorem in Banach spaces that do not contain duals
%J Studia Mathematica
%D 1996
%P 67-85
%V 121
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/sm-121-1-67-85/
%R 10.4064/sm-121-1-67-85
%G en
%F 10_4064_sm_121_1_67_85
Vladimir Fonf; Michael Lin; Alexander Rubinov. On the uniform ergodic theorem in Banach spaces that do not contain duals. Studia Mathematica, Tome 121 (1996) no. 1, pp. 67-85. doi: 10.4064/sm-121-1-67-85

Cité par Sources :