Center and Quasi Center on Banach Normal Hyperalgebra

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.