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Invertibility in rings of the commutator ab-ba, where aba=a and bab=b

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Invertibility in rings of the commutator ab-ba, where aba=a and bab=b

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Benítez López, J.; Liu, X.; Rakocevic, V. (2012). Invertibility in rings of the commutator ab-ba, where aba=a and bab=b. Linear and Multilinear Algebra. 60(4):449-463. https://doi.org/10.1080/03081087.2011.605064

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Título: Invertibility in rings of the commutator ab-ba, where aba=a and bab=b
Autor: Benítez López, Julio Liu, Xiaoji Rakocevic, Vladimir
Entidad UPV: Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
Fecha difusión:
Resumen:
Let R be a ring and a, b is an element of R satisfy aba = a and bab = b. We characterize when ab - ba is invertible. This study is specialized when R has an involution and when b is the Moore-Penrose inverse of a.
Palabras clave: Ring , Involution , Generalized inverses
Derechos de uso: Cerrado
Fuente:
Linear and Multilinear Algebra. (issn: 0308-1087 )
DOI: 10.1080/03081087.2011.605064
Editorial:
Taylor & Francis
Versión del editor: http://dx.doi.org/10.1080/03081087.2011.605064
Código del Proyecto:
info:eu-repo/grantAgreement/MICINN//MTM2010-18539/ES/DISEÑO, ANALISIS Y OPTIMIZACION DE METODOS DE RESOLUCION DE ECUACIONES Y SISTEMAS NO LINEALES. APLICACIONES A PROBLEMAS DE VALOR INICIAL Y FLUJO OPTICO/
info:eu-repo/grantAgreement/MESTD/Basic Research (BR or ON)/174025/RS/Problems in Nonlinear analysis, Operator theory, Topology and applications/
info:eu-repo/grantAgreement/NSFC//11601005/
info:eu-repo/grantAgreement/MOST//210164/
Agradecimientos:
We would like to thank the referee for his/her careful reading. The first author is supported by Spanish Project MTM2010-18539, the second author is supported by the National Natural Science Foundation of China (11601005) ...[+]
Tipo: Artículo

References

Baksalary, J. K., & Baksalary, O. M. (2004). Nonsingularity of linear combinationsof idempotent matrices. Linear Algebra and its Applications, 388, 25-29. doi:10.1016/j.laa.2004.02.025

Ben-Israel, A and Greville, TNE.Generalized Inverses: Theory and Applications, Wiley-Interscience, New York, 1974; 2nd ed., Springer, New York, 2002

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 [+]
Baksalary, J. K., & Baksalary, O. M. (2004). Nonsingularity of linear combinationsof idempotent matrices. Linear Algebra and its Applications, 388, 25-29. doi:10.1016/j.laa.2004.02.025

Ben-Israel, A and Greville, TNE.Generalized Inverses: Theory and Applications, Wiley-Interscience, New York, 1974; 2nd ed., Springer, New York, 2002

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., & Rakočević, V. (2010). Matrices A such that AA†−A†A are nonsingular. Applied Mathematics and Computation, 217(7), 3493-3503. doi:10.1016/j.amc.2010.09.022

Benítez, J., & Rakočević, V. (2010). Invertibility of the commutator of an element in a C*-algebra and its Moore–Penrose inverse. Studia Mathematica, 200(2), 163-174. doi:10.4064/sm200-2-4

Buckholtz, D. (1997). Inverting the Difference of Hilbert Space Projections. The American Mathematical Monthly, 104(1), 60. doi:10.2307/2974825

Buckholtz, D. (2000). Proceedings of the American Mathematical Society, 128(05), 1415-1419. doi:10.1090/s0002-9939-99-05233-8

Gross, J., & Trenkler, G. (2000). Nonsingularity of the Difference of Two Oblique Projectors. SIAM Journal on Matrix Analysis and Applications, 21(2), 390-395. doi:10.1137/s0895479897320277

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

Koliha, J. J., & RakoČević, V. (2002). Invertibility of the Sum of Idempotents. Linear and Multilinear Algebra, 50(4), 285-292. doi:10.1080/03081080290004960

Koliha, J. J., & Rakočević, V. (2003). Invertibility of the Difference of Idempotents. Linear and Multilinear Algebra, 51(1), 97-110. doi:10.1080/030810802100023499

Koliha, J. J., & Rakočević, V. (2004). On the Norm of Idempotents in $C^*$ -Algebras. Rocky Mountain Journal of Mathematics, 34(2), 685-697. doi:10.1216/rmjm/1181069874

Koliha, J. ., Rakočević, V., & Straškraba, I. (2004). The difference and sum of projectors. Linear Algebra and its Applications, 388, 279-288. doi:10.1016/j.laa.2004.03.008

Koliha, J. J., & Rakočević, V. (2006). The nullity and rank of linear combinations of idempotent matrices. Linear Algebra and its Applications, 418(1), 11-14. doi:10.1016/j.laa.2006.01.011

Koliha, J. J., & RakoČević, V. (2007). Range projections and the Moore–Penrose inverse in rings with involution. Linear and Multilinear Algebra, 55(2), 103-112. doi:10.1080/03081080500472954

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