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Almost Convergence, Summability And Ergodicity

Published online by Cambridge University Press:  20 November 2018

J. Peter Duran
J. Peter Duran*
Affiliation:
University of Puerto Rico, Mayaguez, Puerto Rico
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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" semigroup of positive regular matrices in the definition of invariant mean. The resulting "- invariant means" give rise to a summability method which we dub -almost convergence.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 2 , April 1974 , pp. 372 - 387
Copyright
Copyright © Canadian Mathematical Society 1974

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