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Turkish Journal of Mathematics

DOI

-

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.

First Page

163

Last Page

170

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