Extreme Points of Certain Subsets of Hermitian Elements in Banach Algebras

Authors: GERD HERZOG, CHRISTOPH SCHMOEGER

Abstract: We consider the real Banach spaces H(A) of all hermitian elements of a complex Banach algebra A. We prove that if an even power of a \in N(A) is hermitian, then a is an extreme point of the unit ball of H(A) if and only if a^2 = 1. Moreover, if an odd power of a \in H(A) is hermitian and a is an extreme point of the unit ball of H(A), then a^3 = a.

Keywords: Extreme points, hermitian elements

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