A characterization of commutativity for non-associative normed algebras.
A note on Lie nilpotency in operator algebras
A proof of the Russo-Dye theorem for -algebras.
A structure theory for Jordan -pairs
Jordan -pairs appear, in a natural way, in the study of Lie -triple systems ([3]). Indeed, it is shown in [4, Th. 3.1] that the problem of the classification of Lie -triple systems is reduced to prove the existence of certain -algebra envelopes, and it is also shown in [3] that we can associate topologically simple nonquadratic Jordan -pairs to a wide class of Lie -triple systems and then the above envelopes can be obtained from a suitable classification, in terms of associative -pairs, of...
Asymmetric decompositions of vectors in -algebras
By investigating the extent to which variation in the coefficients of a convex combination of unitaries in a unital -algebra permits that combination to be expressed as convex combination of fewer unitaries of the same algebra, we generalise various results of R. V. Kadison and G. K. Pedersen. In the sequel, we shall give a couple of characterisations of -algebras of .
Automatic continuity of biorthogonality preservers between weakly compact JB*-triples and atomic JBW*-triples
We prove that every biorthogonality preserving linear surjection from a weakly compact JB*-triple containing no infinite-dimensional rank-one summands onto another JB*-triple is automatically continuous. We also show that every biorthogonality preserving linear surjection between atomic JBW*-triples containing no infinite-dimensional rank-one summands is automatically continuous. Consequently, two atomic JBW*-triples containing no rank-one summands are isomorphic if and only if there exists a (not...
Axiomatique quantique et algèbres normées non associatives