Extremally rich JB* -triples

Journal Article

2016

Published in: /DOI%3A%2010.1215/20088752-3661557

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.

• Publication Work Type: research paper
• Publisher Name: Tusi Mathematical Research Group
• Volume Number: Volume 7
• Issue Number: 4
• Magazine \ Newspaper: Annals of Functional Analysis
• Pages: 578-592.