Almost everywhere convergence and boundedness of Cesàro-\(\alpha\) ergodic averages (Q1807900)

For positive linear operators \(T:L^p \rightarrow L^p\) the Cesàro\(- \alpha\) average is defined by the formula \[ R_{n, \alpha}f = \frac{1}{A_n^{\alpha}}\sum_{i=0}^nA_{n-i}T^if \] whera \(A_n^{\alpha} =\frac{(\alpha +1) \cdots (\alpha + n)}{ n!}\). In this paper the classical ergodic theorems on the averages \(R_nf = \frac{1}{n+1}\sum_{i=0}^nT^if \) are generalized on the case of \(R_{n, \alpha}\).