Mackey hyperplanes/enlargements for Tweddle's space
type: Item
instance of: scholarly article
title: Mackey hyperplanes/enlargements for Tweddle's space
zbMATH Open document ID: 1308.46004
author: Stephen A. Saxon
published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
publication date: 2014-09-09T00:00:00Z
review text: This paper investigates properties of different classes of locally convex spaces related to barrelled spaces and spaces endowed with the Mackey topology. The motivation for the present research comes from an article by \textit{I. Tweddle} [Indian J. Math. 50, No. 1, 99--114 (2008; Zbl 1157.46002)] that defines locally convex topologies in the Banach space \(\ell_\infty\) of bounded sequences that are complete and Mackey spaces (i.e., they are endowed with their Mackey topology), and satisfy that every hyperplane of the space endowed with this topology is also Mackey. Among other results, the author shows that an example due to \textit{I. Tweddle} and him [Bull. Aust. Math. Soc. 51, No. 3, 521--528 (1995; Zbl 0838.46002)] shares the same behavior. The paper mainly discusses the following question: Let \(E\) be a Mackey space such that its topological dual does not coincide with the algebraic dual. Which is the weakest barrelledness condition on \(E\) to ensure (Q1) that every dense hyperplane is Mackey, (Q2) that at least one dense hyperplane is Mackey? The related question of the existence of Mackey enlargements is also considered. Many properties of Tweddle's examples are analyzed.
reviewed by: José Bonet
Mathematics Subject Classification ID: 46A08
Mathematics Subject Classification ID: 46A20
Mathematics Subject Classification ID: 46A50
Mathematics Subject Classification ID: 46E10
zbMATH DE Number: 6341690
zbMATH Keywords: barrelled spaces
zbMATH Keywords: weakly barrelled spaces
zbMATH Keywords: Mackey topology
zbMATH Keywords: countable enlargements
zbMATH Keywords: tightness
zbMATH Keywords: maximal almost disjoint families
MaRDI profile type: Publication
full work available at URL: s13398-013-0159-x
OpenAlex ID: W2164766074
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DOI: 10.1007/S13398-013-0159-X
description: scientific article; zbMATH DE number 6341690