Multicyclicity of unbounded normal operators and polynomial approximation in \(\mathbb{C}\)
type: Item
instance of: scholarly article
title: Multicyclicity of unbounded normal operators and polynomial approximation in \(\mathbb{C}\)
zbMATH Open document ID: 1175.47021
author: Béla Nagy
published in: Journal of Functional Analysis
publication date: 2009-09-17T00:00:00Z
review text: In [Duke Math.\ J.\ 22, 75--94 (1955; Zbl 0064.11603)], \textit{J.\,Bram} showed that every star-cyclic bounded normal operator \(N\) on a separable Hilbert space \(H\) has a cyclic vector, and that every multiplication operator by the independent variable \(z\) on \(L^2(m)\), for some finite compact measure \(m\), has a cyclic vector in \(L^\infty(m)\). The author of the present paper extends this result to the case of a general unbounded normal operator, implying by this that the classical multiplicity and the multicyclicity of the operator coincide. Furthermore, he obtains a couple of consequences. The proof is a modification and development of Bram's method devloped in the above cited paper, but the extension seems to be far from being obvious and straightforward.
reviewed by: Abdellatif Bourhim
Mathematics Subject Classification ID: 47B15
Mathematics Subject Classification ID: 47B25
Mathematics Subject Classification ID: 47A16
zbMATH DE Number: 5604498
zbMATH Keywords: unbounded normal operator
zbMATH Keywords: star-cyclic vector
zbMATH Keywords: cyclic vector
zbMATH Keywords: multiplicity
zbMATH Keywords: multicyclicity
zbMATH Keywords: polynomial approximation in \(L^{2}(\mathbb{C}, m)\)
zbMATH Keywords: equivalent measures
MaRDI profile type: Publication
full work available at URL: j.jfa.2009.06.028
OpenAlex ID: W2036639712
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DOI: 10.1016/J.JFA.2009.06.028
description: scientific article; zbMATH DE number 5604498