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2015 Non-Synthetic diagonal operators on the space of functions analytic on the unit disk
Kate Overmoyer, Steven M. Seubert
Rocky Mountain J. Math. 45(4): 1233-1244 (2015). DOI: 10.1216/RMJ-2015-45-4-1233

Abstract

Examples are given of continuous operators of functions analytic on the unit disk having the monomials as eigenvectors which fail spectral synthesis (that is, which have closed invariant subspaces which are not the closed linear span of collections of eigenvectors). Examples include the diagonal operator having as eigenvalues an enumeration of $\IL\equiv \{m+in: m,n\in\mathbb{Z}\}$ and diagonal operators having as eigenvalues enumerations of $\{n^{1/p}e^{2\pi ij/3p}: 0\leq j \lt p\}$ where $p$ is an integer at least~2.

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Kate Overmoyer. Steven M. Seubert. "Non-Synthetic diagonal operators on the space of functions analytic on the unit disk." Rocky Mountain J. Math. 45 (4) 1233 - 1244, 2015. https://doi.org/10.1216/RMJ-2015-45-4-1233

Information

Published: 2015
First available in Project Euclid: 2 November 2015

zbMATH: 1325.30057
MathSciNet: MR3418193
Digital Object Identifier: 10.1216/RMJ-2015-45-4-1233

Subjects:
Primary: 30B50, 47A16, 47B38, 47B40

Rights: Copyright © 2015 Rocky Mountain Mathematics Consortium

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Vol.45 • No. 4 • 2015
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