Existence of spectral well-behaved \(\ast\)-representations
type: Item
instance of: scholarly article
title: Existence of spectral well-behaved \(\ast\)-representations
zbMATH Open document ID: 1103.46029
author: S. J. Bhatt
author: M. Fragoulopoulou
author: A. Inoue
published in: Journal of Mathematical Analysis and Applications
publication date: 2006-04-06T00:00:00Z
review text: Given an unbounded \(m^{*}\)-seminorm \(p\) of a \(*\)-algebra, a \(p\)-spectral \(*\)-representation is studied in connection with well-behaved \(*\)-representations. The existence of well-behaved \(p\)-spectral \(*\)-representations on \(*\)-algebras is characterized through certain properties of Ptak functions on the domain of \(p\). Also, the existence of a spectral well-behaved \(*\)-representation of a locally convex \(*\)-algebra is studied in terms of the properties of Ptak functions defined on the \(*\)-subalgebra generated by selfajoint elements of the set of Allan bounded elements. Finally, the authors examine the existence of \(p\)-spectral well-behaved \(*\)-representations in several classes of locally convex \(*\)-algebras.
reviewed by: Dumitru D. Draghia
Mathematics Subject Classification ID: 46K10
zbMATH DE Number: 5017395
zbMATH Keywords: spectral and \(p\)-spectral \(\ast\)-representation
zbMATH Keywords: well-behaved \(\ast\)-representation
zbMATH Keywords: Pták function
zbMATH Keywords: Hermitian algebra
MaRDI profile type: Publication
full work available at URL: j.jmaa.2005.09.016
OpenAlex ID: W2035002686
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DOI: 10.1016/J.JMAA.2005.09.016
description: scientific article; zbMATH DE number 5017395