Isomorphisms of Jordan-Banach algebras.
JB algebras with an exceptional ideal.
JB*-triples have Pelczynski's Property V.
Jordan homomorphisms in proper JCQ-triples.
Jordan polynomials can be analytically recognized
We prove that there exists a real or complex central simple associative algebra M with minimal one-sided ideals such that, for every non-Jordan associative polynomial p, a Jordan-algebra norm can be given on M in such a way that the action of p on M becomes discontinuous.
Lie triple ideals and Lie triple epimorphisms on Jordan and Jordan-Banach algebras
A linear subspace M of a Jordan algebra J is said to be a Lie triple ideal of J if [M,J,J] ⊆ M, where [·,·,·] denotes the associator. We show that every Lie triple ideal M of a nondegenerate Jordan algebra J is either contained in the center of J or contains the nonzero Lie triple ideal [U,J,J], where U is the ideal of J generated by [M,M,M]. Let H be a Jordan algebra, let J be a prime nondegenerate Jordan algebra with extended centroid C and unital central closure Ĵ, and let...
Local and Global Splittings in the State Space of a JB-Algebra.
Modular annihilator Jordan pairs.
Multiplicative characterization of Hilbert spaces and other interesting classes of Banach spaces.
For a Banach space X, we show how the existence of a norm-one element u in X and a norm-one continuous bilinear mapping f: X x X --> X satisfying f(x,u) = f(u,x) = x for all x in X, together with some more intrinsic conditions, can be utilized to characterize X as a member of some relevant subclass of the class of Banach spaces.
Multipliers of JS-Algebras.
Noncommutative Jordan algebras containing minimal inner ideals
Noncommutative Jordan C*-Algebras.
Nuclear JC-algebras and tensor products of types.
On JB*-triples defined by fibre bundles.
On Linear and Quadratic Jordan Division Algebras.
On real Cartan factors.
On Real Forms of JB*-triples.
On the behaviour of Jordan-algebra norms on associative algebras
We prove that for a suitable associative (real or complex) algebra which has many nice algebraic properties, such as being simple and having minimal idempotents, a norm can be given such that the mapping (a,b) ↦ ab + ba is jointly continuous while (a,b) ↦ ab is only separately continuous. We also prove that such a pathology cannot arise for associative simple algebras with a unit. Similar results are obtained for the so-called "norm extension problem", and the relationship between these results...
On the Lie algebra of holomorphic infinitesimal isometries of some classical complex symmetric Banach manifolds
The Banach-Lie algebras ℌκ of all holomorphic infinitesimal isometries of the classical symmetric complex Banach manifolds of compact type (κ = 1) and non compact type (κ = −1) associated with a complex JB*-triple Z are considered and the Lie ideal structure of ℌκ is studied.
On the radical of J*-triples.