The R-quasi center of a Banach Algebra II

Abstract EN

In this paper we show that for a nonunital Banach algebra A ,the set of all p-quasi central elements of A need not be a subset of the set of all p-quasi central elements of A*, where A* is the unitization of A , but under some conditions it will be a subset .

Also we prove that under some conditions the p-quasi centrality is preserved under quotient mapping, and we give two examples to show that for a unital Banach algebra B, Qp(B) need not be closed under addition or under multiplication or topologically closed.