Characterization of the center of a prime Banach algebra by its homoderivations

Résumé

Let X be a Banach algebra. The value of the present article focuses on the fact that, first, it presents detailed informations about zero-power valued maps

on X ,second, it provides characterization to the center of X via its homoderivations. Finally, we include some examples to show that various restrictions in the hypothesis of our theorems are not superfluous.