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On the (C,α) uniform ergodic theorem

100%

Ed-dari E.

Studia Mathematica

2003

tom 156

nr 1

3-13

We improve a recent result of T. Yoshimoto about the uniform ergodic theorem with Cesàro means of order α. We give a necessary and sufficient condition for the (C,α) uniform ergodicity with α > 0.

On the (C,α) Cesàro bounded operators

100%

Ed-dari E.

Studia Mathematica

2004

tom 161

nr 2

163-175

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 $Mₙ^{α} = (Aₙ^{α})^{-1} ∑_{k=0}^{n} A_{n-k}^{α-1}T^{k}$. For α = 1, we find $Mₙ¹ = (n+1)^{-1} ∑_{k=0}^{n}T^{k}$, the usual Cesàro mean. We give necessary and sufficient conditions for a (C,α) bounded operator to be (C,α) strongly (weakly) ergodic.

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2 Studia Mathematica

2 Ed-dari E.

1 2004

1 2003

Wyniki wyszukiwania

On the (C,α) uniform ergodic theorem

On the (C,α) Cesàro bounded operators