Strongly preserver problems in Banach algebras and C1-algebras |
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Authors: | M. Burgos A.C. Márquez-García A. Morales-Campoy |
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Affiliation: | 1. Campus de Jerez, Facultad de Ciencias Sociales y de la Comunicación Av. de la Universidad s/n, 11405 Jerez, Cádiz, Spain;2. Departamento Álgebra y Análisis Matemático, Universidad de Almería, 04120 Almería, Spain |
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Abstract: | Let A and B be Banach algebras. Assume that A is unital. We prove that an additive map strongly preserves Drazin (or equivalently group) invertibility, if and only if T is a Jordan triple homomorphism. When A and B are C1-algebras, we characterize the linear maps strongly preserving generalized invertibility (in the Jordan systems’ sense), and as consequence we determine the structure of selfadjoint linear maps strongly preserving Moore–Penrose invertibility. |
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