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manuscripta mathematica

, Volume 38, Issue 3, pp 381–386 | Cite as

Propriétés Analytiques du Spectre dans les Algèbres de Jordan-Banach

  • Bernard Aupetit
  • Abdelwahab Zraïbi
Article

Abstract

If λ→f(λ) is an analytic function from a domain D of the complex plane into a Jordan-Banach algebra we prove that λ→Sp f(λ) is an analytic multivalued function. From this derives the subharmonicity of λ→Log ρ(f(λ)), where ρ denotes the spectral radius. We apply these results to prove that a Jordan-Banach algebra A is associative if and only if the spectral radius is subadditive and submultiplicative on A and to prove that A/Rad A is isomorphic to the complex plane if and only if each element of A has only one point in its spectrum.

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Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • Bernard Aupetit
    • 1
  • Abdelwahab Zraïbi
    • 1
  1. 1.Département de mathématiquesUniversité LavalQuébecCanada

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