A+ CATEGORY SCIENTIFIC UNIT

On the $(C,\alpha )$ Cesàro bounded operators

Volume 161 / 2004

Elmouloudi Ed-dari Studia Mathematica 161 (2004), 163-175 MSC: 47A35, 47A10. DOI: 10.4064/sm161-2-4

Abstract

For a given linear operator $T$ in a complex Banach space $X$ and $\alpha \in {{\mathbb C}}$ with $\Re (\alpha )>0$, we define the $n$th Cesàro mean of order $\alpha $ of the powers of $T$ by $ M_{n}^{\alpha }=(A_{n}^{\alpha })^{-1} \sum _{k=0}^{n}A_{n-k}^{\alpha -1}T^{k}$. For $\alpha =1$, 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 $(C,\alpha )$ bounded operator to be $(C,\alpha )$ strongly (weakly) ergodic.

Authors

  • Elmouloudi Ed-dariFaculté des sciences Jean Perrin
    Université D'Artois
    SP 18
    62307 Lens Cedex, France
    e-mail

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