Spectral theory for one-parameter groups of isometries
type: Item
instance of: scholarly article
title: Spectral theory for one-parameter groups of isometries
zbMATH Open document ID: 0834.47035
DOI: 10.1016/0022-247X(92)90194-I
published in: Journal of Mathematical Analysis and Applications
publication date: 1993-04-01T00:00:00Z
review text: If \(\{U(t)\}_{t\in \mathbb{R}}\) is a given unitary one-parameter group of operators in Hilbert space, there are well-known \({\mathcal L}^p\)- integrability conditions \((p\geq 1)\) on the imaginary part of the resolvent operators which imply absolute continuity of the spectral resolution for \(\{U(t)\}\). Although one-parameter groups of isometries in Banach space do not in general have spectral resolutions, they still have an attractive spectral theory. In this paper, the author displays resolvent type conditions which imply spectral continuity for such one-parameter groups, thus generalizing the Hilbert space results. The results are applied to the case of one- parameter groups of automorphisms of \(C^*\)-algebras in the last section.
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 46L55
zbMATH DE Number: 150581
zbMATH Keywords: unitary one-parameter group of operators in Hilbert space
zbMATH Keywords: \({\mathcal L}^ p\)-integrability conditions
zbMATH Keywords: absolute continuity of the spectral resolution
zbMATH Keywords: one-parameter groups of isometries in Banach space
zbMATH Keywords: resolvent type conditions
zbMATH Keywords: spectral continuity
zbMATH Keywords: one-parameter groups of automorphisms of \(C^*\)-algebras
author: Palle Jorgensen
MaRDI profile type: Publication
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full work available at URL: 0022-247x(92)90194-i
OpenAlex ID: W2053544109
description: scientific article; zbMATH DE number 150581