Representation theorems on \(w_ 0(\Phi)\) and \(w_ 0^ 0(\Phi)\)
type: Item
instance of: scholarly article
title: Representation theorems on \(w_ 0(\Phi)\) and \(w_ 0^ 0(\Phi)\)
zbMATH Open document ID: 0792.46005
author: Lorna Israel Paredes
published in: Southeast Asian Bulletin of Mathematics
publication date: 1994-07-21T00:00:00Z
review text: Finding representations for continuous linear functionals on function spaces as well as sequence spaces has been the focus of several works in Analysis. In the field of sequence spaces, studies have been made on functionals which are orthogonally additive but not necessarily linear. In particular, the representation theorems for orthogonally additive functionals on the sequence spaces \(\ell_ p\) and \(c_ 0\) were given by \textit{T. S. Chew} and \textit{P. Y. Lee} [ibid. 9, No. 2, 81-85 (1985; Zbl 0613.46007)] and on the space \(w_ 0\) of sequences which are Cesàro strongly summable to zero by \textit{T. S. Chew} [Ann. Soc. Math. Polon., Ser. I, Commentat. Math. 29, No. 2, 149-153 (1990; Zbl 0745.47016)]. In this note, we give a version of the representation theorem for continuous orthogonally additive functionals on the sectionally modulated sequence space \(w_ 0(\Phi)\) and other related spaces.
Mathematics Subject Classification ID: 46A45
Mathematics Subject Classification ID: 46A80
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 563434
zbMATH Keywords: representations for continuous linear functionals
zbMATH Keywords: functionals which are orthogonally additive but not necessarily linear
zbMATH Keywords: orthogonally additive functionals
zbMATH Keywords: continuous orthogonally additive functionals on the sectionally modulated sequence space
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 563434