The algebra of unbounded continuous functions on a Stonean space and unbounded operators
type: Item
instance of: scholarly article
title: The algebra of unbounded continuous functions on a Stonean space and unbounded operators
zbMATH Open document ID: 0977.47019
author: Fotios C. Paliogiannis
published in: Michigan Mathematical Journal
publication date: 2001-01-01T00:00:00Z
review text: A space \(x\) is called extremely disconnected if the closure of every open set is also open, and is a Stonean space if it is also compact and Hausdorff. In this article the author studies the Kadison classes \(N(X)\), \(S(X)\) of normal and selfadjoint functions respectively, these being the unbounded continuous complex-valued and real-valued function on \(X\) respectively. The main results are: a simplified proof of Kadison's result that \(N(X)\) is an algebra, using a result on continuous extensions from open dense subsets of \(X\); an alternative proof of the result that \(S(X)\) is a boundedly complete lattice; a proof of the spectral theorem and characterization of the spectrum and the spectral projections of unbounded selfadjoint operators.
Mathematics Subject Classification ID: 47B25
Mathematics Subject Classification ID: 46J10
Mathematics Subject Classification ID: 47B15
zbMATH DE Number: 1548303
zbMATH Keywords: extremely disconnected spaces
zbMATH Keywords: Stonean space
zbMATH Keywords: Kadison classes
zbMATH Keywords: boundedly complete lattice
zbMATH Keywords: spectral projections of unbounded selfadjoint operators
reviewed by: W. D. Evans
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1030132357
OpenAlex ID: W2042133969
DOI: 10.1307/MMJ/1030132357
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description: scientific article; zbMATH DE number 1548303