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Matrix transformations between some new sequence spaces. (English) Zbl 0542.40003
Let σ be a mapping of the set of positive integers into itself, let V σ be the space of bounded sequences all of whose σ-means are equal, and let σ-lim x be the common value of all σ-means on x. In this paper the author generalizes the idea of strong almost convergence of I. J. Maddox [Math. Proc. Camb. Philos. Soc. 83, 61-64 (1978; Zbl 0392.40001)]: a bounded sequence x=(x k ) is said to be strongly σ-convergent to a number L if and only if (|x k -L|)V σ with σ-limit zero. He characterizes those real infinite matrices which map all convergent sequences (all sequences of σ-bounded variation) into sequences strongly σ-convergent to zero (strongly σ- convergent). The concept of sequences of σ-bounded variation was introduced by the author in an earlier paper [Q. J. Math., Oxf. II. Ser. 34, 77-86 (1983)].
Reviewer: J.Boos

MSC:
40C05Matrix methods in summability
40F05Absolute and strong summability
40C99General summability methods
40D25Inclusion theorems; equivalence theorems