APPROXIMATIONS OF POSITIVE OPERATORS AND CONTINUITY OF THE SPECTRAL RADIUS-III

We prove estimates on the speed of convergence of the 'peripheral eige nvalues' (and principal eigen-vectors) of a sequence T(n) of positive operators on a Banach lattice E to the peripheral eigenvalues of its l imit operator T on E which is positive, irreducible and such that the spectral radius r(T) of T is a Riesz point of the spectrum of T (that is, a pole of the resolvent of T with a residuum of finite rank) under some conditions on the kind of approximation of T(n) to T. These resu lts sharpen results of convergence obtained by the authors in previous papers.