INVARIANT SUBSPACE THEOREMS FOR POSITIVE OPERATORS

We establish new invariant subspace theorems for positive operators on Banach lattices. Here are three sample results. If a quasinilpotent positive operator S dominates a non-zero compact operator K (i.e., \Kx\ less-than-or-equal-to S Absolute value of x for each x), then every positive operator that commutes with S, in particular S itself, has a non-trivial closed invariant ideal. If a positive kernel operator commutes with a quasinilpotent positive operator, then both operators have a common non-trivial closed invariant subspace. Every quasinilpotent positive Dunford-Pettis operator has a non-trivial closed invariant subspace. (C) 1994 Academic Press, Inc.