Extremally rich JB* -triples
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 extreme points of the closed unit ball of E. More concretely, we prove that
dist(a,∂e(E1))=max {1,∥a∥−1}, for every a∈E which is not Brown–Pedersen quasi-invertible. As a consequence, we determine the form of the λ-function of Aron and Lohman on the open unit ball of an extremally rich JB∗-triple E by showing that λ(a)=1/2 for every non-BP quasi-invertible element a in the open unit ball of E. We also prove that for an extremally rich JB∗-triple E, the quadratic conorm γq(⋅) is continuous at a point a∈E if and only if either a is not von Neumann regular (i.e., γq(a)=0) or a is Brown–Pedersen quasi-invertible.
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…