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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| Formato: | JOUR |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00393223_v167_n3_p215_Becker |
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| Sumario: | 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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