Symmetric ideals of generalized summing multilinear operators

Let $X_1,\dots ,X_n,Y$ be classes of Banach spaces-valued sequences. An $n$-linear operator $A$ between Banach spaces belongs to the ideal of $(X_1,\dots ,X_n;Y)$-summing multilinear operators if $(A(x_j^1,\dots ,x_j^n){)}_{j=1}^{\mathrm{\infty }}$ belongs to $Y$ whenever $(x_j^k{)}_{j=1}^{\mathrm{\infty }}$ belongs to $X_k,k=1,\dots ,n$. In this paper we develop techniques to generate non trivial symmetric ideals of this type. Illustrative examples and additional applications of the techniques are provided.