Propriétés Analytiques du Spectre dans les Algèbres de Jordan-Banach

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.