A non-selfadjoint Russo-Dye theorem
type: Item
instance of: scholarly article
title: A non-selfadjoint Russo-Dye theorem
zbMATH Open document ID: 0844.47025
DOI: 10.1007/BF01446314
published in: Mathematische Annalen
publication date: 1996-01-30T00:00:00Z
full work available at URL: https://eudml.org/doc/165424
review text: We prove a Russo-Dye theorem for an infinite multiplicity nest algebra \(\text{Alg } {\mathcal N}\): if \(A\) is an operator in \(\text{Alg } {\mathcal N}\) so that \(|A|< (n-1)/ (n+1)\), then there exist \(16n (n+1)\) unitary operators from \(\text{Alg } {\mathcal N}\) whose mean is equal to \(A\). A similar result is also valid for the algebra of the Cantor nest \({\mathcal N} (\mathbb{Q})\) and other operator algebras. Our results locate the first classes of non-selfadjoint operator algebras for which a Russo-Dye type theorem is valid.
Mathematics Subject Classification ID: 47L30
zbMATH DE Number: 838436
zbMATH Keywords: Russo-Dye theorem
zbMATH Keywords: infinite multiplicity nest algebra
zbMATH Keywords: unitary operators
zbMATH Keywords: algebra of the Cantor nest
zbMATH Keywords: non-selfadjoint operator algebras
zbMATH Keywords: Russo-Dye type theorem
author: Mixalis Anoussis
author: Elias G. Katsoulis
reviewed by: Mixalis Anoussis
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 838436