Geodesic
Some mean and uniform ergodic type theorems
Filomat, Tome 36 (2022) no. 7, p. 2403

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DOI

Let X be a Banach space and T ∈ B(X). Cohen determined a class of regular infinite matrices A = (a nk) for which L n := ∞ k=1 a nk T k converges strongly to an element invariant under T. In the present paper we study A-mean and A-uniform ergodic type results when A = (a nk) is a regular infinite matrix satisfying Cohen's uniformity condition lim j ∞ k= j |a n,k+1 − a nk | = 0, uniformly in n.
DOI : 10.2298/FIL2207403O
Classification : 47A35, 46B15, 40C05
Keywords: Ergodic theorem, mean ergodic theorem, uniform ergodic theorem, ergodic decomposition, Cesàro average, regular matrix, bounded linear operator, power bounded operator 
Gencay Oğuza; Cihan Orhan. Some mean and uniform ergodic type theorems. Filomat, Tome 36 (2022) no. 7, p. 2403 . doi: 10.2298/FIL2207403O
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     title = {Some mean and uniform ergodic type theorems},
     journal = {Filomat},
     pages = {2403 },
     year = {2022},
     volume = {36},
     number = {7},
     doi = {10.2298/FIL2207403O},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2207403O/}
}
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