On the paper: Numerical radius preserving linear maps on Banach algebras

Mohammed El Azhari (1)

1 UM5 - Université Mohammed V de Rabat [Agdal]

We give an example of a unital commutative complex Banach algebra having a normalized state which is not a spectral state and admitting an extreme normalized state which is not multiplicative. This disproves two results by Golfarshchi and Khalilzadeh.

Mots clés: normalized state; regular norm; spectral state; Banach algebra

Domaines: Analyse fonctionnelle [math.FA]

Mohammed El Azhari. On the paper: Numerical radius preserving linear maps on Banach algebras. Mathematics Letters, 2017, 3 (5), pp.50-51. ⟨hal-01292407v2⟩