Spectral properties of self-adjoint subspaces
type: Item
instance of: scholarly article
title: Spectral properties of self-adjoint subspaces
zbMATH Open document ID: 1268.47003
author: Yuming Shi
author: Chunmei Shao
author: Guojing Ren
published in: Linear Algebra and its Applications
publication date: 2013-01-21T00:00:00Z
review text: This paper focuses on spectral properties of self-adjoint subspaces in the product space of a Hilbert space. Several classifications of the spectrum of a self-adjoint subspace are introduced, including discrete spectrum, essential spectrum, continuous spectrum, singular continuous spectrum, absolutely continuous spectrum, and singular spectrum. Relationships between the subspace and its operator part are established, respectively. It is shown that all self-adjoint subspace extensions of a closed Hermitian subspace have the same essential spectrum. As a simple application, it is shown that every self-adjoint subspace extension of the corresponding minimal subspace to a singular second-order symmetric linear difference equation has a bounded spectrum under some conditions. This shows that there is an essential difference between spectral properties of singular symmetric difference operators and classical regular or singular symmetric differential operators.
reviewed by: Bilender P. Allahverdiev
Mathematics Subject Classification ID: 47A06
Mathematics Subject Classification ID: 47A10
Mathematics Subject Classification ID: 47B15
Mathematics Subject Classification ID: 47B25
Mathematics Subject Classification ID: 39A70
zbMATH DE Number: 6127335
zbMATH Keywords: spectrum
zbMATH Keywords: Hermitian subspace
zbMATH Keywords: selfadjoint subspace
zbMATH Keywords: singular symmetric linear difference equation
MaRDI profile type: Publication
full work available at URL: j.laa.2012.07.047
OpenAlex ID: W2038078778
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DOI: 10.1016/J.LAA.2012.07.047
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description: scientific article; zbMATH DE number 6127335