Positive m-homogeneous polynomial ideals

Abstract

We introduce and study the concept of positive polynomial ideals between Banach lattices. The paper develops the basic principles of these classes and presents methods for constructing them from given positive operator ideals. In addition, we present concrete examples of positive polynomial ideals that demonstrate the relevance of these classes. In particular, weintroduce a new class of positive polynomials, referred to as positive (q,r)-dominated polynomials, which constitutes an important example of a positive polynomial ideal.