The centroid of a JB*-triple system.
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.
The Julia-Carathéodory theorem for distance-decreasing maps on infinite dimensional hyperbolic spaces
A classical Julia-Carathéodory theorem concerning radial limits of holomorphic maps in one dimension is extended to hyperbolic contractions of bounded symmetric domains in J*-algebras.
The norm extension problem: positive results and limits.
The range of a derivation on a Jordan-Banach algebra
The questions when a derivation on a Jordan-Banach algebra has quasi-nilpotent values, and when it has the range in the radical, are discussed.
The triple-norm extension problem: the nondegenerate complete case.
We prove that, if A is an associative algebra with two commuting involutions τ and π, if A is a τ-π-tight envelope of the Jordan Triple System T:=H(A,τ) ∩ S(A,π), and if T is nondegenerate, then every complete norm on T making the triple product continuous is equivalent to the restriction to T of an algebra norm on A.
The -function in -algebras.
Théorème de Gelfand-Mazur dans les algèbres p-normées non-associatives.
Théorèmes de factorisation dans les algèbres completes de Jordan.
A generalization of a result of Cohen-Hewitt is given in the case of Jordan-Banach algebras. Some precisions of factorization are obtained.
Théorèmes de factorisation dans les algèbres normées complètes non associatives
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...
Trace and Spectrum Preserving Linear Mappings in Jordan-Banach Algebras.