Spectral measures which fail to be equicontinuous
type: Item
instance of: scholarly article
title: Spectral measures which fail to be equicontinuous
zbMATH Open document ID: 0822.46055
DOI: 10.1007/BF01876370
author: S. Okada
author: Werner J. Ricker
published in: Periodica Mathematica Hungarica
publication date: 1995-10-22T00:00:00Z
review text: Spectral measures, and their equivalent formulation in terms of \(\sigma\)- complete Boolean algebras of projections, play a fundamental role in the spectral theory of normal operators in Hilbert spaces. An essential ingredient in this theory is the uniform boundedness of the spectral measure. It was soon realized that to treat certain operators in Banach spaces such as \(L^ \infty\), the \(\sigma\)-additivity has to be relaxed. This was achieved by using the weak* topology rather than the norm topology of \(L^ \infty\). Here the natural analogue of the uniform boundedness of the projections is the requirement that they form an equicontinuous family of operators. So, granted that there exist non- equicontinuous spectral measures (of interest) the question is, how often they do occur. The aim of this note is to show that they occur frequently in a systematic way.
Mathematics Subject Classification ID: 46G10
Mathematics Subject Classification ID: 47B15
Mathematics Subject Classification ID: 47B40
Mathematics Subject Classification ID: 46A11
zbMATH DE Number: 598225
zbMATH Keywords: spectral measures
zbMATH Keywords: \(\sigma\)-complete Boolean algebras of projections
zbMATH Keywords: spectral theory of normal operators
zbMATH Keywords: uniform boundedness of the spectral measure
zbMATH Keywords: equicontinuous family of operators
reviewed by: Baltasar Rodríguez-Salinas
MaRDI profile type: Publication
cites work: Spectral measures and the Bade reflexivity theorem
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cites work: Q5336643
cites work: On Boolean Algebras of Projections and Scalar-Type Spectral Operators
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cites work: The uniformly closed algebra generated by a complete Boolean algebra of projections
full work available at URL: https://doi.org/10.1007/bf01876370
OpenAlex ID: W2073190442
description: scientific article; zbMATH DE number 598225