On property (Saw) and others spectral properties type Weyl-Browder theorems

An operator T acting on a Banach space X satisfies the property (aw) if σ(T) \ σw(T) = Ea(T), where σw(T) is the Weyl spectrum of T and Eo a(T) is the set of all eigenvalues of T of finite multiplicity that are isolated in the approximate point spectrum of T. In this paper we introduce and study two...

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Autores:
Sanabria, José E.
Carpintero, Carlos R.
Rosas Rodriguez, Ennis Rafael
García, Orlando
Tipo de recurso:
Article of journal
Fecha de publicación:
2017
Institución:
Corporación Universidad de la Costa
Repositorio:
REDICUC - Repositorio CUC
Idioma:
eng
OAI Identifier:
oai:repositorio.cuc.edu.co:11323/2169
Acceso en línea:
https://hdl.handle.net/11323/2169
https://repositorio.cuc.edu.co/
Palabra clave:
A-Weyl's theorem
Property (Sab)
Property (Saw)
Semi B-Fredholm operator
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network_acronym_str RCUC2
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repository_id_str
dc.title.spa.fl_str_mv On property (Saw) and others spectral properties type Weyl-Browder theorems
title On property (Saw) and others spectral properties type Weyl-Browder theorems
spellingShingle On property (Saw) and others spectral properties type Weyl-Browder theorems
A-Weyl's theorem
Property (Sab)
Property (Saw)
Semi B-Fredholm operator
title_short On property (Saw) and others spectral properties type Weyl-Browder theorems
title_full On property (Saw) and others spectral properties type Weyl-Browder theorems
title_fullStr On property (Saw) and others spectral properties type Weyl-Browder theorems
title_full_unstemmed On property (Saw) and others spectral properties type Weyl-Browder theorems
title_sort On property (Saw) and others spectral properties type Weyl-Browder theorems
dc.creator.fl_str_mv Sanabria, José E.
Carpintero, Carlos R.
Rosas Rodriguez, Ennis Rafael
García, Orlando
dc.contributor.author.spa.fl_str_mv Sanabria, José E.
Carpintero, Carlos R.
Rosas Rodriguez, Ennis Rafael
García, Orlando
dc.subject.spa.fl_str_mv A-Weyl's theorem
Property (Sab)
Property (Saw)
Semi B-Fredholm operator
topic A-Weyl's theorem
Property (Sab)
Property (Saw)
Semi B-Fredholm operator
description An operator T acting on a Banach space X satisfies the property (aw) if σ(T) \ σw(T) = Ea(T), where σw(T) is the Weyl spectrum of T and Eo a(T) is the set of all eigenvalues of T of finite multiplicity that are isolated in the approximate point spectrum of T. In this paper we introduce and study two new spectral properties, namely (Saw) and (Sab), in connection with Weyl-Browder type theorems. Among other results, we prove that T satisfies property (Saw) if and only if T satisfies property (aw) and σSBF-+(T) = σw(T), where σSBF-+ (T) is the upper semi B-Weyl spectrum of T.
publishDate 2017
dc.date.issued.none.fl_str_mv 2017
dc.date.accessioned.none.fl_str_mv 2019-01-23T21:57:18Z
dc.date.available.none.fl_str_mv 2019-01-23T21:57:18Z
dc.type.spa.fl_str_mv Artículo de revista
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dc.type.content.spa.fl_str_mv Text
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dc.identifier.issn.spa.fl_str_mv 00347426
dc.identifier.uri.spa.fl_str_mv https://hdl.handle.net/11323/2169
dc.identifier.instname.spa.fl_str_mv Corporación Universidad de la Costa
dc.identifier.reponame.spa.fl_str_mv REDICUC - Repositorio CUC
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identifier_str_mv 00347426
Corporación Universidad de la Costa
REDICUC - Repositorio CUC
url https://hdl.handle.net/11323/2169
https://repositorio.cuc.edu.co/
dc.language.iso.none.fl_str_mv eng
language eng
dc.relation.references.spa.fl_str_mv [1] P. Aiena, Fredholm and Local Spectral Theory, with Applications to Multipliers, Kluwer, 2004. [2] , Quasi-Fredholm operators and localized SVEP, Acta Sci. Math. (Szeged) 73 (2007), 251–263. [3] P. Aiena, E. Aponte, and E. Balzan, Weyl type Theorems for left and right polaroid operators, Integr. Equ. Oper. Theory 66 (2010), 1–20. [4] P. Aiena, M. T. Biondi, and C. Carpintero, On drazin invertibility, Proc. Amer. Math. Soc. 136 (2008), 2839–2848. [5] P. Aiena, C. Carpintero, and E. Rosas, Some characterization of operators satisfying a-Browder’s theorem, J. Math. Anal. Appl. 311 (2005), 530–544. [6] P. Aiena and L. Miller, On generalized a-Browder’s theorem, Studia Math. 180 (2007), 285–299. [7] M. Amouch and M. Berkani, On the property (gw), Mediterr. J. Math. 5 (2008), 371–378. [8] M. Amouch and H. Zguitti, On the equivalence of Browder’s theorem and generalized Browder’s theorem, Glasgow Math. J. 48 (2006), 179–185. [9] M. Berkani, Restriction of an operator to the range of its powers, Studia Math. 140 (2000), 163–175. [10] M. Berkani, M. Kachad, H. Zariouh, and H. Zguitti, Variations on aBrowder-type theorems, Sarajevo J. Math. 9 (2013), 271–281. [11] M. Berkani and J. Koliha, Weyl type theorems for bounded linear operators, Acta Sci. Math. (Szeged) 69 (2003), 359–376. [12] M. Berkani, M. Sarih, and H. Zariouh, Browder-type theorems and SVEP, Mediterr. J. Math. 8 (2011), 399–409. [13] M. Berkani and H. Zariouh, Extended Weyl type theorems, Math. Bohemica 134 (2009), 369–378. [14] , New extended Weyl type theorems, Mat. Vesnik 62 (2010), 145– 154. [15] L. A. Coburn, Weyl’s theorem for nonnormal operators, Michigan Math. J. 13 (1966), 285–288. [16] J. K. Finch, The single valued extension property on a Banach space, Pacific J. Math. 58 (1975), 61–69. [17] A. Gupta and N. Kashayap, Property (Bw) and Weyl type theorems, Bull. Math. Anal. Appl. 3 (2011), 1–7. [18] , Variations on Weyl type theorems, Int. J. Contemp. Math. Sciences 8 (2012), 189–198. [19] V. Rakoˇcevi´c, On a class of operators, Mat. Vesnik 37 (1985), 423–426. [20] , Operators obeying a-Weyl’s theorem, Rev. Roumaine Math. Pures Appl. 34 (1989), 915–919. [21] M. H. M. Rashid, Properties (t) and (gt) for bounded linear operators, Mediterr. J. Math. 11 (2014), 729–744. [22] M. H. M. Rashid and T. Prasad, Variations of Weyl type theorems, Ann Funct. Anal. Math. 4 (2013), 40–52. [23] , Property (Sw) for bounded linear operators, Asia-European J. Math. 8 (2015), 14 pages, DOI: 10.1142/S1793557115500126. [24] J. Sanabria, C. Carpintero, E. Rosas, and O. Garc´ıa, On generalized property (v) for bounded linear operators, Studia Math. 212 (2012), 141–154. [25] H. Zariouh, Property (gz) for bounded linear operators, Mat. Vesnik 65 (2013), 94–103. [26] , New version of property (az), Mat. Vesnik 66 (2014), 317–322. [27] H. Zariouh and H. Zguitti, Variations on Browder’s theorem, Acta Math. Univ. Comenianae 81 (2012), 255–264.
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dc.publisher.spa.fl_str_mv Revista Colombiana de Matematicas
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spelling Sanabria, José E.Carpintero, Carlos R.Rosas Rodriguez, Ennis RafaelGarcía, Orlando2019-01-23T21:57:18Z2019-01-23T21:57:18Z201700347426https://hdl.handle.net/11323/2169Corporación Universidad de la CostaREDICUC - Repositorio CUChttps://repositorio.cuc.edu.co/An operator T acting on a Banach space X satisfies the property (aw) if σ(T) \ σw(T) = Ea(T), where σw(T) is the Weyl spectrum of T and Eo a(T) is the set of all eigenvalues of T of finite multiplicity that are isolated in the approximate point spectrum of T. In this paper we introduce and study two new spectral properties, namely (Saw) and (Sab), in connection with Weyl-Browder type theorems. Among other results, we prove that T satisfies property (Saw) if and only if T satisfies property (aw) and σSBF-+(T) = σw(T), where σSBF-+ (T) is the upper semi B-Weyl spectrum of T.Sanabria, José E.-713a9d59-342c-4562-b3d6-c06f5b214126-0Carpintero, Carlos R.-fe383790-b687-4109-8367-f91f6e274a1c-0Rosas Rodriguez, Ennis Rafael-0000-0001-8123-9344-600García, Orlando-3ec99ae8-85d0-4a8a-a21f-6cc390d93d03-0engRevista Colombiana de MatematicasAtribución – No comercial – Compartir igualinfo:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2A-Weyl's theoremProperty (Sab)Property (Saw)Semi B-Fredholm operatorOn property (Saw) and others spectral properties type Weyl-Browder theoremsArtículo 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 Applications to Multipliers, Kluwer, 2004. [2] , Quasi-Fredholm operators and localized SVEP, Acta Sci. Math. (Szeged) 73 (2007), 251–263. [3] P. Aiena, E. Aponte, and E. Balzan, Weyl type Theorems for left and right polaroid operators, Integr. Equ. Oper. Theory 66 (2010), 1–20. [4] P. Aiena, M. T. Biondi, and C. Carpintero, On drazin invertibility, Proc. Amer. Math. Soc. 136 (2008), 2839–2848. [5] P. Aiena, C. Carpintero, and E. Rosas, Some characterization of operators satisfying a-Browder’s theorem, J. Math. Anal. Appl. 311 (2005), 530–544. [6] P. Aiena and L. Miller, On generalized a-Browder’s theorem, Studia Math. 180 (2007), 285–299. [7] M. Amouch and M. Berkani, On the property (gw), Mediterr. J. Math. 5 (2008), 371–378. [8] M. Amouch and H. Zguitti, On the equivalence of Browder’s theorem and generalized Browder’s theorem, Glasgow Math. J. 48 (2006), 179–185. [9] M. Berkani, Restriction of an operator to the range of its powers, Studia Math. 140 (2000), 163–175. [10] M. Berkani, M. Kachad, H. Zariouh, and H. Zguitti, Variations on aBrowder-type theorems, Sarajevo J. Math. 9 (2013), 271–281. [11] M. Berkani and J. Koliha, Weyl type theorems for bounded linear operators, Acta Sci. Math. (Szeged) 69 (2003), 359–376. [12] M. Berkani, M. Sarih, and H. Zariouh, Browder-type theorems and SVEP, Mediterr. J. Math. 8 (2011), 399–409. [13] M. Berkani and H. Zariouh, Extended Weyl type theorems, Math. Bohemica 134 (2009), 369–378. [14] , New extended Weyl type theorems, Mat. Vesnik 62 (2010), 145– 154. [15] L. A. Coburn, Weyl’s theorem for nonnormal operators, Michigan Math. J. 13 (1966), 285–288. [16] J. K. Finch, The single valued extension property on a Banach space, Pacific J. Math. 58 (1975), 61–69. [17] A. Gupta and N. Kashayap, Property (Bw) and Weyl type theorems, Bull. Math. Anal. Appl. 3 (2011), 1–7. [18] , Variations on Weyl type theorems, Int. J. Contemp. Math. Sciences 8 (2012), 189–198. [19] V. Rakoˇcevi´c, On a class of operators, Mat. Vesnik 37 (1985), 423–426. [20] , Operators obeying a-Weyl’s theorem, Rev. Roumaine Math. Pures Appl. 34 (1989), 915–919. [21] M. H. M. Rashid, Properties (t) and (gt) for bounded linear operators, Mediterr. J. Math. 11 (2014), 729–744. [22] M. H. M. Rashid and T. Prasad, Variations of Weyl type theorems, Ann Funct. Anal. Math. 4 (2013), 40–52. [23] , Property (Sw) for bounded linear operators, Asia-European J. Math. 8 (2015), 14 pages, DOI: 10.1142/S1793557115500126. [24] J. Sanabria, C. Carpintero, E. Rosas, and O. Garc´ıa, On generalized property (v) for bounded linear operators, Studia Math. 212 (2012), 141–154. [25] H. Zariouh, Property (gz) for bounded linear operators, Mat. Vesnik 65 (2013), 94–103. [26] , New version of property (az), Mat. Vesnik 66 (2014), 317–322. [27] H. Zariouh and H. Zguitti, Variations on Browder’s theorem, Acta Math. Univ. Comenianae 81 (2012), 255–264.PublicationORIGINALOn property (Saw) and others spectral properties type Weyl-Browder theorems.pdfOn property (Saw) and others spectral properties type Weyl-Browder theorems.pdfapplication/pdf1393448https://repositorio.cuc.edu.co/bitstreams/3e765def-a45e-4f87-8fd9-4986fe60b00d/download8cdc5de60046ad9ae296bea0ab7fa919MD51LICENSElicense.txtlicense.txttext/plain; charset=utf-81748https://repositorio.cuc.edu.co/bitstreams/3a30dd4a-c240-4b01-833d-f7c50208bc30/download8a4605be74aa9ea9d79846c1fba20a33MD52THUMBNAILOn property (Saw) and others spectral properties type Weyl-Browder theorems.pdf.jpgOn property (Saw) and others spectral properties type Weyl-Browder theorems.pdf.jpgimage/jpeg38999https://repositorio.cuc.edu.co/bitstreams/f0c543c1-933f-45a2-8777-659c33d997af/download56d59c95a01e4d1859f971c3020d281dMD54TEXTOn property (Saw) and others spectral properties type Weyl-Browder theorems.pdf.txtOn property (Saw) and others spectral properties type Weyl-Browder theorems.pdf.txttext/plain34688https://repositorio.cuc.edu.co/bitstreams/1507ebf8-7839-44a9-93bb-9084acd3cab1/downloadb03deca22aaaab9c1020a0302efe82f0MD5511323/2169oai:repositorio.cuc.edu.co:11323/21692024-09-17 11:04:29.858open.accesshttps://repositorio.cuc.edu.coRepositorio de la Universidad de la Costa CUCrepdigital@cuc.edu.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