Automorphisms on a C*-algebra and isomorphisms between Lie JC*-algebras associated with a generalized additive mapping

• Autores: Chun-Gil Park
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 33, Nº 3, 2007, págs. 815-837
• Idioma: inglés
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• Resumen

  • It is shown that if an odd mapping satisfies a generalized additive functional equation, then the odd mapping is Cauchy additive, and we prove the Cauchy-Rassias stability of linear mappings in Banach modules over a unital C*-algebra for the generalized additive functional equation. As an application, we show that every almost linear bijective mapping on a unital C*-algebra is an automorphism under some conditions, and that every almost linear bijective mapping of a unital Lie JC*-algebra onto a unital Lie JC*-algebra is a Lie JC*-algebra isomorphism under some conditions.