On non-degenerate Jordan triple systems
We demonstrate that all JB*-triples (hence, all JB∗-algebras and all C*-algebras) are non-degenerate Jordan triple systems but a Jordan triple system may not be non-degenerate; any two elements x and y in a non-degenerate Jordan triple system are von Neumann regular with generalized inverses of each other whenever the induced Bergmann operator B(x, y) (or equivalently, B(y, x)) vanishes; however, the converse is not true even in case of C*-algebras. L. G. Brown and G. K. Pedersen introduced a notion of quasi-invertible elements in a C*-algebra, which plays a significant role in studying geometry of the unit ball. Recently, the present authors began a study of BP-quasi invertible elements in the general setting of JB*-triples; here, it is deduced further that B(x, y) on a JB*-triple J vanishes if and only if x and y are BP-quasi inverses of each other. Thus, von Neumann regularity for BP-quasi invertible elements in a JB*-triple is a necessity but not a sufficiency
We establish new estimates to compute the λ-function of Aron and Lohman on the unit ball of a
JB*-triple. It is established that for every Brown–Pedersen quasi-invertible element a in a JB*-…
We introduce and study the class of extremally rich JB∗-triples. We establish new results to determine the distance from an element a in an extremally rich JB∗-triple E to the set ∂e(E1) of all…
The aim of this note is to study Cebyšëv JB*-subtriples of general JB*-triples. It is established that if F is a non-zero Cebyšëv JB*-subtriple of a JB*-triple E, then exactly one of the following…