Extreme Points of Certain Subsets of Hermitian Elements in Banach Algebras

Authors : Gerd HERZOG, Christoph SCHMOEGER

Pages : 163-170

View : 13 | Download : 4

Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :We consider the real Banach spaces Hinsert ignore into journalissuearticles values(A); of all hermitian elements of a complex Banach algebra A. We prove that if an even power of a \in Ninsert ignore into journalissuearticles values(A); is hermitian, then a is an extreme point of the unit ball of Hinsert ignore into journalissuearticles values(A); if and only if a2 = 1. Moreover, if an odd power of a \in Hinsert ignore into journalissuearticles values(A); is hermitian and a is an extreme point of the unit ball of Hinsert ignore into journalissuearticles values(A);, then a3 = a.
Keywords : Extreme points, hermitian elements