Large structures within the class of summing operators (Q6110809)

The main goal of this paper is to contribute to the research of lineability and spaceability for classes of multilinear operators. The main result is the pointwise $\mathfrak{c}$-spaceability of classes of $\Lambda $-summing operators. Also, the authors prove that some sets of operators taking values in spaces of general $q$-summable scalar families $\ell _{q}(I) $ can be $(\alpha,\mathrm{card}\,I)$-lineable, for some infinite set $I$ and some cardinal $\alpha<\mathrm{card}\, I$.