An-Najah University Journal for Research - A (Natural Sciences)

Article info

Keywords

• quasi-center
• Banach hyperalgbera
• center
• normal hyperalgebra
• Hahn Banach Theorem

Abstract

In this paper, we prove that every strongly distributive hyperalgebra is normal. Also, we prove that if X is a normed normal hyperalgebra with a propertyza◦x.zb◦y = zab◦xy and |λ| > ‖x‖, then (zλ◦e − x) is invertible. Moreover, we give a characterization of the center of a unital complex Banach normal hyperalgebra with the same property. Finally, we define the quasi-center, σ-quasi center and ρ-quasi center of Banach normal hyperalgebra as a generalization of the center and study some basic properties and relations between them.

معلومات المقال

الكلمات الإفتتاحية

• quasi-center
• Banach hyperalgbera
• center
• normal hyperalgebra
• Hahn Banach Theorem

الملخص

In this paper, we prove that every strongly distributive hyperalgebra is normal. Also, we prove that if X is a normed normal hyperalgebra with a propertyza◦x.zb◦y = zab◦xy and |λ| > ‖x‖, then (zλ◦e − x) is invertible. Moreover, we give a characterization of the center of a unital complex Banach normal hyperalgebra with the same property. Finally, we define the quasi-center, σ-quasi center and ρ-quasi center of Banach normal hyperalgebra as a generalization of the center and study some basic properties and relations between them.