Représentations unitaires et opérateurs à trace. (Unitary representations and traceable operators)
type: Item
instance of: scholarly article
title: Représentations unitaires et opérateurs à trace. (Unitary representations and traceable operators)
zbMATH Open document ID: 0647.22006
DOI: 10.1016/0022-1236(88)90087-0
author: Nouri Kamoun
published in: Journal of Functional Analysis
publication date: 1988-01-01T00:00:00Z
review text: The author proves the following generalization of Theorem 4.2.2 of \textit{N. V. Pedersen} [Math. Ann. 247, 191-244 (1980; Zbl 0406.22008)]. Theorem. Let G be a connected simply connected Lie group and let \({\mathfrak g}\) be its algebra. There exists a non-zero semi-invariant P in S(\({\mathfrak g}_{{\mathbb{C}}})\) (we denote by w the semi-invariant of U(\({\mathfrak g}_{{\mathbb{C}}})\) corresponding to P and by O the set \(\{\ell \in g^*_{{\mathbb{C}}}:\) \(P(-i\ell)=0\})\), such that: for every normal factorial representation \(\pi\) of G, for which there are f in O and \(\tau \in X_ G^{irr}(f)\) with \(\ker\pi= \ker T^ T_{f,\tau}\), we have: \(\pi(w*\phi)\) is traceable relative to the factor \(\pi(G)''\) generated by \(\pi(G)\), where \(\phi\) is an arbitrary element of \({\mathcal D}(G)\).
Mathematics Subject Classification ID: 22E45
zbMATH DE Number: 4055936
zbMATH Keywords: connected simply connected Lie group
zbMATH Keywords: semi-invariant
zbMATH Keywords: normal factorial representation
reviewed by: S. V. Kislyakov
MaRDI profile type: Publication
full work available at URL: 0022-1236(88)90087-0
OpenAlex ID: W2043299456
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description: scientific article; zbMATH DE number 4055936