On \((C,\alpha)\)-summability almost everywhere of certain sequences
In the first part of this paper the author gives a new proof of a result concerning the \((C,\alpha)\)-summability of a sequence of identically distributed independent random numbers and its generalization to sequences of martingale differences. In the second part he considers conditions of \((C, \alpha)\)-summability a.e. of a sequence of powers of the operator \((T^ nf)\), and proves the equivalence of the Cesàro \((C,\alpha)\)-method for all \(\alpha > 1/2\) and the Abel method in the problem of convergence a.e. for any normal contraction in \(L_ 2\).
scientific article; zbMATH DE number 589629
scientific article