Perturbation of m-Isometries by Nilpotent Operators

We prove that if T is an m-isometry on a Hilbert space and Q an n-nilpotent operator commuting with T, then T+Q is a 2n+m-2-isometry. Moreover, we show that a similar result for m, q-isometries on Banach spaces is not true.

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Main Authors: Teresa Bermúdez, Antonio Martinón, Vladimir Müller, Juan Agustín Noda
Format: Article
Language:English
Published: Wiley 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/745479
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author Teresa Bermúdez
Antonio Martinón
Vladimir Müller
Juan Agustín Noda
author_facet Teresa Bermúdez
Antonio Martinón
Vladimir Müller
Juan Agustín Noda
author_sort Teresa Bermúdez
collection DOAJ
description We prove that if T is an m-isometry on a Hilbert space and Q an n-nilpotent operator commuting with T, then T+Q is a 2n+m-2-isometry. Moreover, we show that a similar result for m, q-isometries on Banach spaces is not true.
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series Abstract and Applied Analysis
spelling doaj-art-39e8312cec8a4b7c9e0c7774df83df592025-08-20T03:35:50ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/745479745479Perturbation of m-Isometries by Nilpotent OperatorsTeresa Bermúdez0Antonio Martinón1Vladimir Müller2Juan Agustín Noda3Departamento de Análisis Matemático, Universidad de La Laguna, La Laguna, 38271 Tenerife, SpainDepartamento de Análisis Matemático, Universidad de La Laguna, La Laguna, 38271 Tenerife, SpainMathematical Institute, Czech Academy of Sciences, 115 67 Prague, Czech RepublicDepartamento de Análisis Matemático, Universidad de La Laguna, La Laguna, 38271 Tenerife, SpainWe prove that if T is an m-isometry on a Hilbert space and Q an n-nilpotent operator commuting with T, then T+Q is a 2n+m-2-isometry. Moreover, we show that a similar result for m, q-isometries on Banach spaces is not true.http://dx.doi.org/10.1155/2014/745479
spellingShingle Teresa Bermúdez
Antonio Martinón
Vladimir Müller
Juan Agustín Noda
Perturbation of m-Isometries by Nilpotent Operators
Abstract and Applied Analysis
title Perturbation of m-Isometries by Nilpotent Operators
title_full Perturbation of m-Isometries by Nilpotent Operators
title_fullStr Perturbation of m-Isometries by Nilpotent Operators
title_full_unstemmed Perturbation of m-Isometries by Nilpotent Operators
title_short Perturbation of m-Isometries by Nilpotent Operators
title_sort perturbation of m isometries by nilpotent operators
url http://dx.doi.org/10.1155/2014/745479
work_keys_str_mv AT teresabermudez perturbationofmisometriesbynilpotentoperators
AT antoniomartinon perturbationofmisometriesbynilpotentoperators
AT vladimirmuller perturbationofmisometriesbynilpotentoperators
AT juanagustinnoda perturbationofmisometriesbynilpotentoperators