Centrality in BL (X), The Banach algebra of bounded linear operators

Abstract

In this paper we show that for a complex Banach algebra A = BL(X) of all bounded linear operators on the Banach space X, the set of all rho-quasi central elements of A is a subset of each of. (i) the set of all discrete rho-quasi central elements; (U) the set of all continuous rho-quasi central elements; (W) the set of all residual rho-quasi central elements; and (iv) the set of all approximate discrete rho-quasi central elements of A, and this set inclusion may be proper, but in the case that X is finite dimensional we see that the set of all discrete rho-quasi central elements, the set of all approximate discrete rho-quasi central elements and the set of all rho-quasi central elements of A all are identical, in the other hand the set of all continuous rho-quasi central elements, the set of all residual rho-quasi central elements of A and A are equal. Also we show that any normal operator on a Hilbert space H is a residual rho-quasi …