Two-norm convergence and Tauberian boundedness theorems
type: Item
instance of: scholarly article
title: Two-norm convergence and Tauberian boundedness theorems
zbMATH Open document ID: 0657.40003
published in: Functiones et Approximatio. Commentarii Mathematici
publication date: 1987-01-01T00:00:00Z
review text: Two-norm convergence has turned out to be a very valuable tool in functional analysis and its applications. For example, two-norm convergence in the proper or generalised sense combines a boundedness property and a limit concept [see \textit{J. B. Cooper}, Saks spaces and applications to functional analysis, (1978; Zbl 0379.46005)] and \textit{A. Wilansky} [Summability through functional analysis. (1984; Zbl 0531.40008)]. The authors first introduce B-perfect and BM-perfect methods which are defined by using a two-norm convergence. Using these notations the authors investigate interesting relations between Tauberian boundedness conditions and Tauberian convergence conditions.
Mathematics Subject Classification ID: 40D20
Mathematics Subject Classification ID: 40E05
Mathematics Subject Classification ID: 40H05
Mathematics Subject Classification ID: 40F05
zbMATH DE Number: 4073640
zbMATH Keywords: B-perfect method
zbMATH Keywords: two-norm convergence
zbMATH Keywords: BM-perfect methods
zbMATH Keywords: Tauberian boundedness conditions
zbMATH Keywords: Tauberian convergence conditions
author: Amnon Jakimovski
author: Werner Meyer-König
author: Karl Zeller
reviewed by: H. P. Dikshit
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4073640