A condition equivalent to uniform ergodicity
Let T be a linear operator on a Banach space X with supn ∥Tn/nw∥ < ∞ for some 0 ≤ w < 1. We show that the following conditions are equivalent: (i) n-1 ∑k=0 n-1 Tk converges uniformly; (ii) cl (I-T)X = {z∈X: limn k=1 n Tk z/k exists}.
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00393223_v167_n3_p215_Becker |
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todo:paper_00393223_v167_n3_p215_Becker2023-10-03T14:49:44Z A condition equivalent to uniform ergodicity Becker, M.E. Let T be a linear operator on a Banach space X with supn ∥Tn/nw∥ < ∞ for some 0 ≤ w < 1. We show that the following conditions are equivalent: (i) n-1 ∑k=0 n-1 Tk converges uniformly; (ii) cl (I-T)X = {z∈X: limn k=1 n Tk z/k exists}. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00393223_v167_n3_p215_Becker |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| description |
Let T be a linear operator on a Banach space X with supn ∥Tn/nw∥ < ∞ for some 0 ≤ w < 1. We show that the following conditions are equivalent: (i) n-1 ∑k=0 n-1 Tk converges uniformly; (ii) cl (I-T)X = {z∈X: limn k=1 n Tk z/k exists}. |
| format |
JOUR |
| author |
Becker, M.E. |
| spellingShingle |
Becker, M.E. A condition equivalent to uniform ergodicity |
| author_facet |
Becker, M.E. |
| author_sort |
Becker, M.E. |
| title |
A condition equivalent to uniform ergodicity |
| title_short |
A condition equivalent to uniform ergodicity |
| title_full |
A condition equivalent to uniform ergodicity |
| title_fullStr |
A condition equivalent to uniform ergodicity |
| title_full_unstemmed |
A condition equivalent to uniform ergodicity |
| title_sort |
condition equivalent to uniform ergodicity |
| url |
http://hdl.handle.net/20.500.12110/paper_00393223_v167_n3_p215_Becker |
| work_keys_str_mv |
AT beckerme aconditionequivalenttouniformergodicity AT beckerme conditionequivalenttouniformergodicity |
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1807321917384818688 |