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.