On the (C,α) Cesàro bounded operators

Elmouloudi Ed-dari. "On the (C,α) Cesàro bounded operators." Studia Mathematica 161.2 (2004): 163-175. <http://eudml.org/doc/285056>.

@article{ElmouloudiEd2004,
abstract = {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.},
author = {Elmouloudi Ed-dari},
journal = {Studia Mathematica},
keywords = {Cesàro means; Cesàro bounded operators; ; )},
language = {eng},
number = {2},
pages = {163-175},
title = {On the (C,α) Cesàro bounded operators},
url = {http://eudml.org/doc/285056},
volume = {161},
year = {2004},
}

TY - JOUR
AU - Elmouloudi Ed-dari
TI - On the (C,α) Cesàro bounded operators
JO - Studia Mathematica
PY - 2004
VL - 161
IS - 2
SP - 163
EP - 175
AB - 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.
LA - eng
KW - Cesàro means; Cesàro bounded operators; ; )
UR - http://eudml.org/doc/285056
ER -