Decomposability of Positive Operators on Banach Lattices

    • Jahandideh, M. T., (1997)  Decomposability of Positive Operators on Banach Lattices, Presented in  Symposium of Operator Theory, Queen’s University/Kingston/Canada.

This talk deals with invariant ideals for families of positive operators on Banach lattices. In particular  it studies ideal-decomposable and ideal-triangularizable semigroups of positive operators. We show that in certain Banach lattices compactness is not required for the existence of hyperinvariant closed  ideals for a quasinilpotent positive operator. We also show that in those Banach lattices a semigroup of quasinilpotent positive operators might be decomposable without imposing any compactness condition. We generalize the fact that  the only irreducible C_p-closed subalgebra of C_p is C_p,  itself to extend some recent reducibility results and apply them to derive some decomposability theorems concerning a collection of quasinilpotent positive operators on reflexive Banach lattices.