ON THE APPROXIMATION OF POSITIVE OPERATORS AND THE BEHAVIOR OF THE SPECTRA OF THE APPROXIMANTS

Let T be a positive linear operator on the Banach lattice E and let (S -n) be a sequence of bounded linear operators on E which converge stro ngly to T. Our main results are concerned with the question under whic h additional assumptions on S-n and T the peripheral spectra pi sigma( S-n) of S-n converge to the peripheral spectrum pi sigma(T) of T. We a re able to treat even the more general case of discretely convergent s equences of operators.