On Composition Ideals of Multilinear Mappings and Homogeneous Polynomials

Abstract

Given an operator ideal $\mathcal{I}$, we study the multi-ideal $\mathcal{I}\circ \mathcal{L}$ and the polynomial ideal $\mathcal{I}\circ \mathcal{P}$. The connection with the linearizations of these mappings on projective symmetric tensor products is investigated in detail. Applications to the ideals of strictly singular and absolutely summing linear operators are obtained.