On the hereditary character of certain spectral properties and some applications
In this paper we study the behavior of certain spectral properties of an operator T on a proper closed and T-invariant subspace W ⊆ X such that T n(X) ⊆ W, for some n ≥ 1, where T ∈ L(X) and X is an infinite-dimensional complex Banach space. We prove that for these subspaces a large number of spectr...
- Autores:
-
Carpintero, Rafael
ROSAS, ENNIS
García, Orlando
Sanabria, José
Malaver, Andrés
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2021
- Institución:
- Corporación Universidad de la Costa
- Repositorio:
- REDICUC - Repositorio CUC
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.cuc.edu.co:11323/8836
- Acceso en línea:
- https://hdl.handle.net/11323/8836
https://doi.org/10.22199/issn.0717-6279-3678
https://repositorio.cuc.edu.co/
- Palabra clave:
- Weyl type theorems
Restrictions of operators
Integral operators
Spectral properties
Semi-Fredholm theory
- Rights
- openAccess
- License
- CC0 1.0 Universal
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On the hereditary character of certain spectral properties and some applications |
| title |
On the hereditary character of certain spectral properties and some applications |
| spellingShingle |
On the hereditary character of certain spectral properties and some applications Weyl type theorems Restrictions of operators Integral operators Spectral properties Semi-Fredholm theory |
| title_short |
On the hereditary character of certain spectral properties and some applications |
| title_full |
On the hereditary character of certain spectral properties and some applications |
| title_fullStr |
On the hereditary character of certain spectral properties and some applications |
| title_full_unstemmed |
On the hereditary character of certain spectral properties and some applications |
| title_sort |
On the hereditary character of certain spectral properties and some applications |
| dc.creator.fl_str_mv |
Carpintero, Rafael ROSAS, ENNIS García, Orlando Sanabria, José Malaver, Andrés |
| dc.contributor.author.spa.fl_str_mv |
Carpintero, Rafael ROSAS, ENNIS García, Orlando Sanabria, José Malaver, Andrés |
| dc.subject.spa.fl_str_mv |
Weyl type theorems Restrictions of operators Integral operators Spectral properties Semi-Fredholm theory |
| topic |
Weyl type theorems Restrictions of operators Integral operators Spectral properties Semi-Fredholm theory |
| description |
In this paper we study the behavior of certain spectral properties of an operator T on a proper closed and T-invariant subspace W ⊆ X such that T n(X) ⊆ W, for some n ≥ 1, where T ∈ L(X) and X is an infinite-dimensional complex Banach space. We prove that for these subspaces a large number of spectral properties are transmitted from T to its restriction on W and vice-versa. As consequence of our results, we give conditions for which semi-Fredholm spectral properties, as well as Weyl type theorems, are equivalent for two given operators. Additionally, we give conditions under which an operator acting on a subspace can be extended on the entire space preserving the Weyl type theorems. In particular, we give some applications of these results for integral operators acting on certain functions spaces. |
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2021 |
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2021-11-05T13:58:44Z |
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2021 |
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Artículo de revista |
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0716-0917 0717-6279 |
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https://hdl.handle.net/11323/8836 |
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https://doi.org/10.22199/issn.0717-6279-3678 |
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Corporación Universidad de la Costa |
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REDICUC - Repositorio CUC |
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eng |
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[1] P. Aiena, Fredholm and local spectral theory, with application to multipliers. Dordrecht: Springer, 2004. [2] P. Aiena, “Quasi-Fredholm operators and localized SVEP”, Acta scientiarum mathematicarum, vol. 73, no. 1, pp. 251-263, 2007. [3] P. Aiena, M. T. Biondi, and C. Carpintero, “On Drazin invertibility”, Proceeding of the American Mathematical Society, vol. 136, no. 8, pp. 2839-2848, 2008. [4] F. Astudillo-Villalba and J. Ramos-Fernández, “Multiplication operators on the space of functions of bounded variation”, Demonstratio mathematica, vol. 50, no. 1, pp. 105-115, 2017 [5] B. Barnes, “The spectral and Fredholm theory of extensions of bounded linear operators”, Proceeding of the American Mathematical Society, vol. 105, no. 4, pp. 941-949, 1989. [6] B. Barnes, “Restrictions of bounded linear operators: closed range”, Proceeding of the American Mathematical Society, vol. 135, no. 6, pp. 1735-1740, 2007. [7] M. Berkani, “Restriction of an operator to the range of its powers”, Studia mathematica, vol. 140, no. 2, pp. 163-175, 2000. [8] M. Berkani, “On a class of quasi-Fredholm operators”, Integral equations and operator theory, vol. 34, no. 1, pp. 244-249, 1999. [9] M. Berkani and M. Sarih, “On semi B-Fredholm operators”, Glasgow mathematical journal, vol. 43, no. 3, pp. 457-465, 2001. [10] M. Berkani and H. Zariouh, “Extended Weyl type theorems”, Mathematica bohemica, vol. 134, no. 4, pp. 369-378, 2009. [11] M. Berkani and J. Koliha, “Weyl type theorems for bounded linear operators”, Acta scientiarum mathematicarum, vol. 69, no. 1-2, pp. 359-376, 2003. [12] M. Berkani and H. Zariouh, “New extended Weyl type theorems”, Matematički vesnik, vol. 62, no. 2, pp. 145-154, 2010. [13] M. Berkani, M. Sarih, and H. Zariouh, “Browder-type theorems and SVEP”, Mediterranean journal of mathematics, vol. 8, pp. 399-409, 2011. [14] C. Carpintero, A. Gutiérrez, E. Rosas, y J. Sanabria, “A note on preservation of generalized Fredholm spectra in Berkani’s sense”, Filomat, vol. 32, no. 18, pp. 6431-6440, 2018. [15] L. A. Coburn, “Weyl’s theorem for nonnormal operators”, Michigan mathematical journal, vol. 13, no. 3, pp. 285-288, 1966. [16] L. Chen and W. Su, “A note on Weyl-type theorems and restrictions”, Annals of functional analysis, vol. 8, no. 2, pp. 190-198, 2017. [17] J. K. Finch, “The single valued extension property on a Banach space”, Pacific journal of mathematics, vol. 58, no. 1, pp. 61-69, 1975. [18] A. Gupta and K. Mamtani, “Weyl-type theorems for restrictions of closed linear unbounded operators”, Acta Universitatis Matthiae Belii. Series mathematics, no. 2015, pp. 72-79, 2015. [19] R. E. Harte and W. Y. Lee, “Another note on Weyl’s theorem”, Transactions of the American Mathematical Society, vol. 349, no. 5, pp. 2115-2124, 1997. [20] H. Heuser, Functional analysis. New York, NY: Marcel Dekker, 1982. [21] E. Hewitt and K. A. Ross, Abstract harmonic analysis, vol. 1. Berlin: Springer, 1963. [22] K. Jörgens, Linear integral operator. Boston, MA: Pitman, 1982. [23] V. Rakočević, “Operators obeying a-Weyl’s theorem”, Revue Roumaine de Mathématique Pures et Appliquées, vol. 34, no. 10, pp. 915-919, 1989. [24] V. Rakočević, “On a class of operators”, Matematički vesnik, vol. 37, no. 4, pp. 423-425, 1985. [25] J. Sanabria, C. Carpintero, E. Rosas, and O. García, “On generalized property (v) for bounded linear operators”, Studia mathematica, vol. 212, pp. 141-154, 2012. [26] H. Zariouh, “Property (gz) for bounded linear operators”, Matematički vesnik, vol. 65, no. 1, pp. 94-103, 2013. [27] H. Zariouh, “New version of property (az)”, Matematički vesnik, vol. 66, no. 3, pp. 317-322, 2014. [28] H. Weyl, “Über beschränkte quadratische formen, deren differenz vollstetig ist”, Rendiconti del Circolo Matematico di Palermo, vol. 27, pp. 373-392, 1909. |
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Carpintero, RafaelROSAS, ENNISGarcía, OrlandoSanabria, JoséMalaver, Andrés2021-11-05T13:58:44Z2021-11-05T13:58:44Z20210716-09170717-6279https://hdl.handle.net/11323/8836https://doi.org/10.22199/issn.0717-6279-3678Corporación Universidad de la CostaREDICUC - Repositorio CUChttps://repositorio.cuc.edu.co/In this paper we study the behavior of certain spectral properties of an operator T on a proper closed and T-invariant subspace W ⊆ X such that T n(X) ⊆ W, for some n ≥ 1, where T ∈ L(X) and X is an infinite-dimensional complex Banach space. We prove that for these subspaces a large number of spectral properties are transmitted from T to its restriction on W and vice-versa. As consequence of our results, we give conditions for which semi-Fredholm spectral properties, as well as Weyl type theorems, are equivalent for two given operators. Additionally, we give conditions under which an operator acting on a subspace can be extended on the entire space preserving the Weyl type theorems. In particular, we give some applications of these results for integral operators acting on certain functions spaces.Carpintero, Rafael-will be generated-orcid-0000-0003-2790-5160-600ROSAS, ENNIS-will be generated-orcid-0000-0001-8123-9344-600García, Orlando-will be generated-orcid-0000-0001-7235-2847-600Sanabria, José-will be generated-orcid-0000-0002-9749-4099-600Malaver, Andrés-will be generated-orcid-0000-0001-9986-5116-600application/pdfengCorporación Universidad de la CostaCC0 1.0 Universalhttp://creativecommons.org/publicdomain/zero/1.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Proyeccioneshttps://www.revistaproyecciones.cl/article/view/3678Weyl type theoremsRestrictions of operatorsIntegral operatorsSpectral propertiesSemi-Fredholm theoryOn the hereditary character of certain spectral properties and some applicationsArtículo de revistahttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARTinfo:eu-repo/semantics/acceptedVersion[1] P. Aiena, Fredholm and local spectral theory, with application to multipliers. Dordrecht: Springer, 2004.[2] P. Aiena, “Quasi-Fredholm operators and localized SVEP”, Acta scientiarum mathematicarum, vol. 73, no. 1, pp. 251-263, 2007.[3] P. Aiena, M. T. Biondi, and C. Carpintero, “On Drazin invertibility”, Proceeding of the American Mathematical Society, vol. 136, no. 8, pp. 2839-2848, 2008.[4] F. Astudillo-Villalba and J. Ramos-Fernández, “Multiplication operators on the space of functions of bounded variation”, Demonstratio mathematica, vol. 50, no. 1, pp. 105-115, 2017[5] B. Barnes, “The spectral and Fredholm theory of extensions of bounded linear operators”, Proceeding of the American Mathematical Society, vol. 105, no. 4, pp. 941-949, 1989.[6] B. Barnes, “Restrictions of bounded linear operators: closed range”, Proceeding of the American Mathematical Society, vol. 135, no. 6, pp. 1735-1740, 2007.[7] M. Berkani, “Restriction of an operator to the range of its powers”, Studia mathematica, vol. 140, no. 2, pp. 163-175, 2000.[8] M. Berkani, “On a class of quasi-Fredholm operators”, Integral equations and operator theory, vol. 34, no. 1, pp. 244-249, 1999.[9] M. Berkani and M. Sarih, “On semi B-Fredholm operators”, Glasgow mathematical journal, vol. 43, no. 3, pp. 457-465, 2001.[10] M. Berkani and H. Zariouh, “Extended Weyl type theorems”, Mathematica bohemica, vol. 134, no. 4, pp. 369-378, 2009.[11] M. Berkani and J. Koliha, “Weyl type theorems for bounded linear operators”, Acta scientiarum mathematicarum, vol. 69, no. 1-2, pp. 359-376, 2003.[12] M. Berkani and H. Zariouh, “New extended Weyl type theorems”, Matematički vesnik, vol. 62, no. 2, pp. 145-154, 2010.[13] M. Berkani, M. Sarih, and H. Zariouh, “Browder-type theorems and SVEP”, Mediterranean journal of mathematics, vol. 8, pp. 399-409, 2011.[14] C. Carpintero, A. Gutiérrez, E. Rosas, y J. Sanabria, “A note on preservation of generalized Fredholm spectra in Berkani’s sense”, Filomat, vol. 32, no. 18, pp. 6431-6440, 2018.[15] L. A. Coburn, “Weyl’s theorem for nonnormal operators”, Michigan mathematical journal, vol. 13, no. 3, pp. 285-288, 1966.[16] L. Chen and W. Su, “A note on Weyl-type theorems and restrictions”, Annals of functional analysis, vol. 8, no. 2, pp. 190-198, 2017.[17] J. K. Finch, “The single valued extension property on a Banach space”, Pacific journal of mathematics, vol. 58, no. 1, pp. 61-69, 1975.[18] A. Gupta and K. Mamtani, “Weyl-type theorems for restrictions of closed linear unbounded operators”, Acta Universitatis Matthiae Belii. Series mathematics, no. 2015, pp. 72-79, 2015.[19] R. E. Harte and W. Y. Lee, “Another note on Weyl’s theorem”, Transactions of the American Mathematical Society, vol. 349, no. 5, pp. 2115-2124, 1997.[20] H. Heuser, Functional analysis. New York, NY: Marcel Dekker, 1982.[21] E. Hewitt and K. A. Ross, Abstract harmonic analysis, vol. 1. Berlin: Springer, 1963.[22] K. Jörgens, Linear integral operator. Boston, MA: Pitman, 1982.[23] V. Rakočević, “Operators obeying a-Weyl’s theorem”, Revue Roumaine de Mathématique Pures et Appliquées, vol. 34, no. 10, pp. 915-919, 1989.[24] V. Rakočević, “On a class of operators”, Matematički vesnik, vol. 37, no. 4, pp. 423-425, 1985.[25] J. Sanabria, C. Carpintero, E. Rosas, and O. García, “On generalized property (v) for bounded linear operators”, Studia mathematica, vol. 212, pp. 141-154, 2012.[26] H. Zariouh, “Property (gz) for bounded linear operators”, Matematički vesnik, vol. 65, no. 1, pp. 94-103, 2013.[27] H. Zariouh, “New version of property (az)”, Matematički vesnik, vol. 66, no. 3, pp. 317-322, 2014.[28] H. Weyl, “Über beschränkte quadratische formen, deren differenz vollstetig ist”, Rendiconti del Circolo Matematico di Palermo, vol. 27, pp. 373-392, 1909.PublicationORIGINALOn the hereditary character of certain spectral properties and some applications.pdfOn the hereditary character of certain spectral properties and some applications.pdfapplication/pdf234996https://repositorio.cuc.edu.co/bitstreams/22a1ca35-2b30-4c4a-907f-0ab7b0d57312/downloada42eeb7431dbc7aacdceb8ced0b2f33eMD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8701https://repositorio.cuc.edu.co/bitstreams/3bf6fae6-d77a-46fe-be71-26d8f702d08b/download42fd4ad1e89814f5e4a476b409eb708cMD52LICENSElicense.txtlicense.txttext/plain; charset=utf-83196https://repositorio.cuc.edu.co/bitstreams/3127eecc-b21f-456d-ab2d-7a84a611540f/downloade30e9215131d99561d40d6b0abbe9badMD53THUMBNAILOn the hereditary character of certain spectral properties and some applications.pdf.jpgOn the hereditary character of certain spectral 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