  We investigate the decomposability of nonnegative compact r-potent operators
on a separable Hilbert space L2(X). We provide a constructive algorithm to
prove that basis functions of range spaces of nonnegative r-potent operators
can be chosen to be all nonnegative and mutually orthogonal. We use this
orthogonality to establish that nonnegative compact r-potent operators with
range spaces of dimension strictly greater than r-1 are decomposable.
