Gerd HERZOG, Christoph SCHMOEGER

3414

Extreme Points of Certain Subsets of Hermitian Elements in Banach Algebras

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 a2 = 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 a3 = a.
Anahtar Kelimeler:

Extreme points, hermitian elements

Extreme Points of Certain Subsets of Hermitian Elements in Banach Algebras

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 a2 = 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 a3 = a.
Keywords:

Extreme points, hermitian elements,

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Turkish Journal of Mathematics-Cover
  • ISSN: 1300-0098
  • Yayın Aralığı: Yılda 6 Sayı
  • Yayıncı: TÜBİTAK
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