A Tauberian theorem related to almost convergence
type: Item
instance of: scholarly article
title: A Tauberian theorem related to almost convergence
zbMATH Open document ID: 0751.40002
DOI: 10.1016/0019-3577(91)90033-4
author: Ivor J. Maddox
published in: Indagationes Mathematicae. New Series
publication date: 1992-09-27T00:00:00Z
review text: Define \(A_ n^ \alpha=(\alpha+1)\ldots(\alpha+n)/n!\) and \(a_{nk}=A_{n-k}^{\alpha-1}/A_ n^ \alpha\). For a sequence \((s_ k)\) in any Banach space the summability method \(f_ A\) is defined by \(s_ k\to s(f_ A)\) if uniformly in \(p\geq 0\), \(\sum^ n_{k=0}a_{nk}s_{k+p}\to s\). For \(\alpha=1\) this convergence is known as almost convergence. For \(p=0\) one obtains \((C,\alpha)\)- convergence. The author shows that norm boundedness of the power sequence \((x^ k)\) is a Tauberian condition for its \((C,\alpha)\) summability to imply its \(f_{(C,\alpha)}\) summability.
reviewed by: J. L. Teugels
Mathematics Subject Classification ID: 40A05
Mathematics Subject Classification ID: 46B45
Mathematics Subject Classification ID: 40E05
zbMATH DE Number: 60870
zbMATH Keywords: Cesàro summability
zbMATH Keywords: almost convergence
MaRDI profile type: Publication
full work available at URL: 0019-3577(91)90033-4
OpenAlex ID: W2064218319
cites work: Q5788558
cites work: Remarks on Ergodic Theorems
cites work: A contribution to the theory of divergent sequences
cites work: On Kuttner's Theorem
description: scientific article; zbMATH DE number 60870