Abstract
We investigate lineability/spaceability problems within the setting of multilinear summing operators on quasi-Banach sequence spaces. Furthermore, we deal with the contemporary geometric notions of pointwise-lineability and (α,β)-lineability. Among other results, we prove that the class of multilinear operators taking values on ℓq(0<q≤∞) that are absolutely but not multiple summing is pointwise c-spaceable when non-empty. Spaceability in other classes, such as Dunford-Pettis operators and multilinear operators on general summable scalar families, is also studied.
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