The uniformly closed algebra generated by a complete Boolean algebra of projections
type: Item
instance of: scholarly article
title: The uniformly closed algebra generated by a complete Boolean algebra of projections
zbMATH Open document ID: 0655.47038
DOI: 10.1007/BF01214906
author: Werner J. Ricker
author: Helmut H. Schaefer
published in: Mathematische Zeitschrift
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/174063
review text: The main result established is that the weak operator closed algebra generated by a complete, equicontinuous Boolean algebra of projections in locally convex space X coincides with the closed algebra that it generates with respect to the topology of uniform convergence on the bounded sets of X. For X a Banach space, in which case the topology of uniform convergence on the bounded sets of X is just the uniform operator topology, this is a classical result due to W. G. Bade. The proof of the main result, which is based on the theory of integration with respect to spectral measures, is new even in the Banach space setting.
Mathematics Subject Classification ID: 47L10
zbMATH DE Number: 4069649
zbMATH Keywords: weak operator closed algebra generated by a complete equicontinuous Boolean algebra of projections in a locally convex space
zbMATH Keywords: closed algebra
zbMATH Keywords: topology of uniform convergence on the bounded sets
zbMATH Keywords: uniform operator topology
zbMATH Keywords: integration with respect to spectral measures
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4069649