Trace and Spectrum Preserving Linear Mappings in Jordan-Banach Algebras.
Ume généralisation du théorême d'extension de Radó.
Recent trends in the field of Jordan-Banach algebras
Continuité et uniforme continuité du spectre dans les algèbras de Banach
An improvement of Kaplansky's lemma on locally algebraic operators
On log-subharmonicity of singular values of matrices
Let F be an analytic function from an open subset Ω of the complex plane into the algebra of n×n matrices. Denoting by the decreasing sequence of singular values of a matrix, we prove that the functions and are subharmonic on Ω for 1 ≤ k ≤ n.
Some uses of subharmonicity in functional analysis
Sur les conjectures de Hirschfeld et Zelazko dans les algèbres de Banach
Caractérisation des éléments quasi-nil-potents dans les algèbres de Banach
Utilizzando il teorema di Oka-Rothstein per le funzioni sottoarmoniche e quello di Vesentini sulla sottoarmonicità del raggio spettrale nelle algebre di Banach, si dimostra un teorema di continuità del raggio spettrale. Questo viene poi applicato per dedurne una caratterizzazione degli elementi quasi—nilpotenti ed una nuova dimostrazione del teorema di Kleinecke-Slirokov, assieme ad altri risultati di tipo analogo.
Propriétés analytiques du spèctre dans les algèbres de Jordan-Banach.
Trace and determinant in Banach algebras
We show that the trace and the determinant on a semisimple Banach algebra can be defined in a purely spectral and analytic way and then we obtain many consequences from these new definitions.
The continuity of Lie homomorphisms
We prove that the separating space of a Lie homomorphism from a Banach algebra onto a Banach algebra is contained in the centre modulo the radical.
Distribution des valeurs des fonctions analytiques multiformes
Trace and determinant in Jordan-Banach algebras.
Using an appropriate definition of the multiplicity of a spectral value, we introduce a new definition of the trace and determinant of elements with finite spectrum in Jordan-Banach algebras. We first extend a result obtained by J. Zemánek in the associative case, on the connectedness of projections which are close to each other spectrally (Theorem 2.3). Secondly we show that the rank of the Riesz projection associated to a finite-rank element a and a finite subset of its spectrum is equal to the...
Le grand théorème de Picard pour les multifonctions analytiques finies
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