On the Invariance of the Conservative Ideals of Positive Operators

We extend several results concerning the properties of the conservative and the dissipative ideals of positive operators in Riesz spaces which we have obtained earlier. The main result of the paper consists in a theorem which offers a set of conditions less restrictive than the ones known so far for the invariance of the conservative ideals; the theorem enables us to show that certain properties of the conservative and the dissipative ideals are valid in more general settings than the known ones. While proving the main theorem, we obtain a new proof of an earlier result. We also discuss several examples which motivate the study carried over in the paper.