The spectral properties of [Formula: see text] -complex symmetric operators

In this paper, we introduce the class of [m]-complex symmetric operators and study various properties of this class. In particular, we show that if T is an [m]-complex symmetric operator, then [Formula: see text] is also an [m]-complex symmetric operator for any [Formula: see text] . In addition, we...

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Autor principal: Shen, Junli
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2018
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6096912/
https://www.ncbi.nlm.nih.gov/pubmed/30839552
http://dx.doi.org/10.1186/s13660-018-1800-1
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author Shen, Junli
author_facet Shen, Junli
author_sort Shen, Junli
collection PubMed
description In this paper, we introduce the class of [m]-complex symmetric operators and study various properties of this class. In particular, we show that if T is an [m]-complex symmetric operator, then [Formula: see text] is also an [m]-complex symmetric operator for any [Formula: see text] . In addition, we prove that if T is an [m]-complex symmetric operator, then [Formula: see text] , [Formula: see text] , [Formula: see text] , and [Formula: see text] are symmetric about the real axis. Finally, we investigate the stability of an [m]-complex symmetric operator under perturbation by nilpotent operators commuting with T.
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spelling pubmed-60969122018-08-24 The spectral properties of [Formula: see text] -complex symmetric operators Shen, Junli J Inequal Appl Research In this paper, we introduce the class of [m]-complex symmetric operators and study various properties of this class. In particular, we show that if T is an [m]-complex symmetric operator, then [Formula: see text] is also an [m]-complex symmetric operator for any [Formula: see text] . In addition, we prove that if T is an [m]-complex symmetric operator, then [Formula: see text] , [Formula: see text] , [Formula: see text] , and [Formula: see text] are symmetric about the real axis. Finally, we investigate the stability of an [m]-complex symmetric operator under perturbation by nilpotent operators commuting with T. Springer International Publishing 2018-08-14 2018 /pmc/articles/PMC6096912/ /pubmed/30839552 http://dx.doi.org/10.1186/s13660-018-1800-1 Text en © The Author(s) 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Shen, Junli
The spectral properties of [Formula: see text] -complex symmetric operators
title The spectral properties of [Formula: see text] -complex symmetric operators
title_full The spectral properties of [Formula: see text] -complex symmetric operators
title_fullStr The spectral properties of [Formula: see text] -complex symmetric operators
title_full_unstemmed The spectral properties of [Formula: see text] -complex symmetric operators
title_short The spectral properties of [Formula: see text] -complex symmetric operators
title_sort spectral properties of [formula: see text] -complex symmetric operators
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6096912/
https://www.ncbi.nlm.nih.gov/pubmed/30839552
http://dx.doi.org/10.1186/s13660-018-1800-1
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