Core theorems for subsequences of double complex sequences
type: Item
instance of: scholarly article
title: Core theorems for subsequences of double complex sequences
zbMATH Open document ID: 1228.40007
author: Harry I. Miller
author: Leila Miller-Van Wieren
published in: Bulletin of the Belgian Mathematical Society - Simon Stevin
publication date: 2011-07-11T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.bbms/1307452084
review text: The authors prove core theorems for double sequences with complex entries. These results extend the work of \textit{H. I. Miller} and \textit{R. F. Patterson} [Acta Math. Hung. 119, No. 1--2, 71--80 (2008; Zbl 1212.42021)] dealing with double sequences of real numbers. The authors give an answer to the question ``If \(w\) is a bounded double sequence with complex entries and \(A\) is a four-dimensional matrix summability method, under what conditions on \(A\) does there exist \(z\), a subsequence (rearrangement), of \(w\) such that each complex number \(t\) in the core of \(w\) is a limit point of \(Az\)?''.
reviewed by: Umit Totur
Mathematics Subject Classification ID: 40D25
Mathematics Subject Classification ID: 40G99
Mathematics Subject Classification ID: 28A12
Mathematics Subject Classification ID: 40B05
zbMATH DE Number: 5919209
zbMATH Keywords: double complex sequence
zbMATH Keywords: core
zbMATH Keywords: Pringsheim limit
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5919209