PERIPHERAL SPECTRUM OF POSITIVE QUASI-COMPACT OPERATORS ON C-0(X)

Let X be a locally compact space, and T, a quasi-compact positive oper ator on C-0(X), with positive spectral radius, r. Then the peripheral spectrum of T is a finite set of poles containing r, and the residue o f the resolvent of T at each peripheral pole is of finite rank. Using the concept of closed absorbing set, we develop an iterative process t hat gives the order, p, of r, some special bases of the algebraic eige nspaces ker(T - r)(p) and ker(T - r)(p), and finally the dimension of the algebraic eigenspace associated to each peripheral pole.