Bade-property; survey and comparison with λ-property, Russo-Dye Theorem and Extremally richness
In this article, we survey a geometric property, called Bade-property,
originally introduced by William Bade. First, we review Bade’s work in normed
linear spaces. Next, we illustrate various interesting results of Bade-property in
the spaces of convergent sequences established by Aizpuru. Then, we investigate
Bade-property in comparison with some other geometric properties, such as λ-
property due to Aron and Lohman, Russo-Dye Theorem and extremally richness in
C∗-algebras, JB∗-algebrs/triples and JBW ∗-triples.
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…