Annals of Functional Analysis

Advances in almost convergence

Chao You

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‎In this paper‎, ‎we first give the concept of properly distributed‎ ‎sequence‎, ‎and prove that it is almost convergent with F-limit‎ ‎expressed as a formal integral‎. ‎Basing on these‎, ‎we review the work‎ ‎of Feng and Li‎, ‎which is shown to be a special case of our‎ ‎generalized theory‎. ‎Then we generalize Banach limit to Banach limit‎ ‎functional‎, ‎which is the minimum requirement to characterize strong‎ ‎almost convergence for bounded sequences in normed vector space‎. ‎With this machinery‎, ‎we show that Hajdukovi\'{c}'s almost‎ ‎convergence and quasi-almost convergence are both equivalent to our‎ ‎strong almost convergence‎.

Article information

Ann. Funct. Anal. Volume 3, Number 1 (2012), 49-66.

First available in Project Euclid: 12 May 2014

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46B45: Banach sequence spaces [See also 46A45]
Secondary: 11K36: Well-distributed sequences and other variations

Banach limit functional ‎properly distributed sequence ‎strong almost convergence


You, Chao. Advances in almost convergence. Ann. Funct. Anal. 3 (2012), no. 1, 49--66. doi:10.15352/afa/1399900023.

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