Ideals of polynomials generated by weakly compact operators

Abstract

The aim of these notes is to describe the properties and the relationships between the classes of homogeneous polynomials between Banach spaces which are generated by the ideal of all weakly compact operators, namely, the class of weakly compact polynomials and the class of polynomials which the factorization and the linearization methods generate by the ideal of all weakly compact operators. Containment relationships with ideals of absolutely summing polynomials are also investigated.