On the (C,α) Cesàro bounded operators

Elmouloudi Ed-dari

Studia Mathematica, Tome 162 (2004), p. 163-175 / Harvested from The Polish Digital Mathematics Library

Résumé

For a given linear operator T in a complex Banach space X and α ∈ ℂ with ℜ (α) > 0, we define the nth Cesàro mean of order α of the powers of T by $M ₙ^{α} = {(A ₙ^{α})}^{- 1} \sum_{k = 0}^{n} A_{n - k}^{α - 1} T^{k}$ . For α = 1, we find $M ₙ ¹ = {(n + 1)}^{- 1} \sum_{k = 0}^{n} T^{k}$ , the usual Cesàro mean. We give necessary and sufficient conditions for a (C,α) bounded operator to be (C,α) strongly (weakly) ergodic.

Publié le : 2004-01-01

Zbl 1063.47006

EUDML-ID : urn:eudml:doc:285056

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     title = {On the (C,$\alpha$) Ces\`aro bounded operators},
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     year = {2004},
     pages = {163-175},
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Elmouloudi Ed-dari. On the (C,α) Cesàro bounded operators. Studia Mathematica, Tome 162 (2004) pp. 163-175. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm161-2-4/