Almost Convergence, Summability And Ergodicity
- 1 April 1974
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 26 (02) , 372-387
- https://doi.org/10.4153/cjm-1974-039-6
Abstract
The notion of almost convergence introduced by Lorentz [15] has been generalized in several directions (see, for example [1; 8; 11 ; 14; 17]). I t is the purpose of this paper to give a generalization based on the original definition in terms of invariant means. This is effected by replacing the shift transformation by an "ergodic" semigroupof positive regular matrices in the definition of invariant mean. The resulting "- invariant means" give rise to a summability method which we dub-almost convergence.Keywords
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