ALMOST CONVERGENCE THROUGH THE GENERALIZED DE LA VALLÉE-POUSSIN MEAN

Abstract

Lorentz characterized the almost convergence through the concept of uniform convergence of de laVallée-Poussin mean. In this paper, we generalize the notion of almost convergence by using the concept ofinvariant mean and the generalized de la Vallée-Poussin mean. We determine the bounded linear operators forthe generalized σ-conservative, σ-regular and σ-coercive matrices.