A note on a paper by W. J. Ricker and H. H. Schaefer
type: Item
instance of: scholarly article
title: A note on a paper by W. J. Ricker and H. H. Schaefer
zbMATH Open document ID: 0669.47026
DOI: 10.1007/BF02570762
author: B. de Pagter
published in: Mathematische Zeitschrift
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/174153
review text: In this paper we extend, and present a relatively short proof of a result of \textit{W. J. Ricker} and \textit{H. H. Schaefer} [The uniformly closed algebra generated by a complete Boolean algebra of projections, preprint. Math. Z. (to appear; Zbl 0655.47038)]. In fact it is shown that if X is a quasi-complete locally convex space, and if \({\mathcal A}\) is a Bade-complete equicontinuous Boolean algebra of projections in X, then the strongly closed algebra generated by \({\mathcal A}\) equals the closed algebra generated by \({\mathcal A}\) with respect to the topology of uniform convergence on bounded subsets of X.
Mathematics Subject Classification ID: 47L10
zbMATH DE Number: 4096201
zbMATH Keywords: quasi-complete locally convex space
zbMATH Keywords: Bade-complete equicontinuous Boolean algebra of projections
zbMATH Keywords: topology of uniform convergence on bounded subsets
MaRDI profile type: Publication
cites work: Reflexivity and Order Properties of Scalar-Type Spectral Operators in Locally Convex Spaces
cites work: Q5638775
cites work: The uniformly closed algebra generated by a complete Boolean algebra of projections
cites work: Q3669960
OpenAlex ID: W1967400549
description: scientific article; zbMATH DE number 4096201