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: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/745479 |
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| _version_ | 1849408290035859456 |
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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. |
| format | Article |
| id | doaj-art-39e8312cec8a4b7c9e0c7774df83df59 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| 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 |
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