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1. CMB 1997 (vol 40 pp. 488)

Maouche, Abdelaziz
Caractérisations spectrales du radical et du socle d'une paire de jordan-banach
If $f$ and $g$ are two analytic functions from a domain $D$ of the complex plane into respectively the Banach spaces $V^+$ and $V^-$, we prove that $\lambda\mapsto \Sp\bigl(f(\lambda),g(\lambda)\bigr)$ is an analytic multivalued function. From this derives the subharmonicity of the functions $\lambda\mapsto \rho_V\bigl(f(\lambda),g(\lambda)\bigr)$ and $\lambda\mapsto \log\rho_V\bigl(f(\lambda),g(\lambda)\bigr)$ where $\rho$ denotes the spectral radius. We apply these results to obtain nice caracterizations of the radical and the socle of a Banach Jordan pair, and finally we get an algebraic structural theorem.

Keywords:Spectre, rayon spectral, multifonction analytique, quasi-inverse,, paire de Jordan-Banach, radical de Jacobson, socle.
Categories:46H70, (17A15)

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