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Additive results for the group inverse in an algebra with applications to block operators

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Additive results for the group inverse in an algebra with applications to block operators

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Benítez López, J.; Liu, X.; Zhu, T. (2011). Additive results for the group inverse in an algebra with applications to block operators. Linear and Multilinear Algebra. 59(3):279-289. https://doi.org/10.1080/03081080903410262

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Título: Additive results for the group inverse in an algebra with applications to block operators
Autor: Benítez López, Julio Liu, Xiaoji Zhu, Tongping
Entidad UPV: Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
Fecha difusión:
Resumen:
We derive a very short expression for the group inverse of a(1) + ... + a(n) when a(1), ... , a(n) are elements in an algebra having group inverse and satisfying a(i)a(j) = 0 for i < j. We apply this formula in order to ...[+]
Palabras clave: Algebra , Block operators , Group inverse
Derechos de uso: Reserva de todos los derechos
Fuente:
Linear and Multilinear Algebra. (issn: 0308-1087 )
DOI: 10.1080/03081080903410262
Editorial:
Taylor & Francis
Versión del editor: http://dx.doi.org/10.1080/03081080903410262
Código del Proyecto:
info:eu-repo/grantAgreement/Natural Science Foundation of Guangxi Province//0640016/
info:eu-repo/grantAgreement/Natural Science Foundation of Guangxi Province//0832084/
Agradecimientos:
X. Liu and T. Zhu are supported by Guangxi Science Foundation (0640016, 0832084).
Tipo: Artículo

References

Benítez, J. (2008). Moore–Penrose inverses and commuting elements of <mml:math altimg=«si1.gif» overflow=«scroll» xmlns:xocs=«http://www.elsevier.com/xml/xocs/dtd» xmlns:xs=«http://www.w3.org/2001/XMLSchema» xmlns:xsi=«http://www.w3.org/2001/XMLSchema-instance» xmlns=«http://www.elsevier.com/xml/ja/dtd» xmlns:ja=«http://www.elsevier.com/xml/ja/dtd» xmlns:mml=«http://www.w3.org/1998/Math/MathML» xmlns:tb=«http://www.elsevier.com/xml/common/table/dtd» xmlns:sb=«http://www.elsevier.com/xml/common/struct-bib/dtd» xmlns:ce=«http://www.elsevier.com/xml/common/dtd» xmlns:xlink=«http://www.w3.org/1999/xlink» xmlns:cals=«http://www.elsevier.com/xml/common/cals/dtd»><mml:msup><mml:mi>C</mml:mi><mml:mo>∗</mml:mo></mml:msup></mml:math>-algebras. Journal of Mathematical Analysis and Applications, 345(2), 766-770. doi:10.1016/j.jmaa.2008.04.062

Benítez, J, Liu, X and Zhu, T.Nonsingularity and group invertibility of linear combinations of two k-potent matrices, Linear Multilinear Algebra (accepted)

Castro-González, N., Dopazo, E., & Martínez-Serrano, M. F. (2009). On the Drazin inverse of the sum of two operators and its application to operator matrices. Journal of Mathematical Analysis and Applications, 350(1), 207-215. doi:10.1016/j.jmaa.2008.09.035 [+]
Benítez, J. (2008). Moore–Penrose inverses and commuting elements of <mml:math altimg=«si1.gif» overflow=«scroll» xmlns:xocs=«http://www.elsevier.com/xml/xocs/dtd» xmlns:xs=«http://www.w3.org/2001/XMLSchema» xmlns:xsi=«http://www.w3.org/2001/XMLSchema-instance» xmlns=«http://www.elsevier.com/xml/ja/dtd» xmlns:ja=«http://www.elsevier.com/xml/ja/dtd» xmlns:mml=«http://www.w3.org/1998/Math/MathML» xmlns:tb=«http://www.elsevier.com/xml/common/table/dtd» xmlns:sb=«http://www.elsevier.com/xml/common/struct-bib/dtd» xmlns:ce=«http://www.elsevier.com/xml/common/dtd» xmlns:xlink=«http://www.w3.org/1999/xlink» xmlns:cals=«http://www.elsevier.com/xml/common/cals/dtd»><mml:msup><mml:mi>C</mml:mi><mml:mo>∗</mml:mo></mml:msup></mml:math>-algebras. Journal of Mathematical Analysis and Applications, 345(2), 766-770. doi:10.1016/j.jmaa.2008.04.062

Benítez, J, Liu, X and Zhu, T.Nonsingularity and group invertibility of linear combinations of two k-potent matrices, Linear Multilinear Algebra (accepted)

Castro-González, N., Dopazo, E., & Martínez-Serrano, M. F. (2009). On the Drazin inverse of the sum of two operators and its application to operator matrices. Journal of Mathematical Analysis and Applications, 350(1), 207-215. doi:10.1016/j.jmaa.2008.09.035

González, N. C., & Koliha, J. J. (2004). New additive results for the g-Drazin inverse. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 134(6), 1085-1097. doi:10.1017/s0308210500003632

Cvetković-Ilić, D. S., Djordjević, D. S., & Wei, Y. (2006). Additive results for the generalized Drazin inverse in a Banach algebra. Linear Algebra and its Applications, 418(1), 53-61. doi:10.1016/j.laa.2006.01.015

Deng, C. Y. (2009). The Drazin inverses of sum and difference of idempotents. Linear Algebra and its Applications, 430(4), 1282-1291. doi:10.1016/j.laa.2008.10.017

Deng, C, Cvetković-Ilić, DS and Wei, Y.Some results on the generalized Drazin inverse of operator matrices, Linear Multilinear Algebra (2009). DOI: 10.1080/03081080902722642

Djordjević, D. S., & Wei, Y. (2002). Additive results for the generalized Drazin inverse. Journal of the Australian Mathematical Society, 73(1), 115-126. doi:10.1017/s1446788700008508

Hartwig, R. E., Wang, G., & Wei, Y. (2001). Some additive results on Drazin inverse. Linear Algebra and its Applications, 322(1-3), 207-217. doi:10.1016/s0024-3795(00)00257-3

Koliha, J. J. (2000). Elements of C*-algebras commuting with their Moore-Penrose inverse. Studia Mathematica, 139(1), 81-90. doi:10.4064/sm-139-1-81-90

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