Separation of the Sturm-Liouville differential operator with an operator potential

In this paper we have studied the separation property of the Sturm-Liouville differential operator with operator potential of the form Ay(x) = -d/dx{[}mu(x)dy/dx] + V(x)y(x) (1) in the space H-p(R), for p = 1, 2, where mu(x) is an element of C-1(R) is a positive continuous function on R and the potential V(x) is an element of L(lambda(p)) is a bounded linear operator on lambda(p). (C) 2003 Published by Elsevier Inc.