Bade-Property; Survey and Comparison with λ-Property, Russo-Dye Theorem and Extremally Richness

Abstract

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.

Key words and phrases. Bade-prpperty, extreme points of the closed unit ball, λ-property.

2000 Mathematics Subject Classification. 17Cxx, 46Bxx, 46B20