• ### Note on the Relation Between Cesaro Averages for Discrete Weighted Shift Operator and the Behavior of the Resolvent

Ali A. Shukur

Department of functional analysis, Belarusian State University, St.Nisovizimosti 4, 22003, Minsk, Belarus.

Abstract: The behavior of the limit of the Cesaro averages was studied in different ergodic theorems. In this note we study these averages for discrete weighted shift operators. The relation between the coefficients of the mentioned operators, the behavior of the Cesaro averages and the behavior of the resolvent is given.

Keywords: Cesaro averages, power-bounded operator, Kriess resolvent condition, Ritt resolvent condition, weighted shift operator.