The area of research called “Lineability” looks for linear structures inside exotic subsets of vector spaces. In the last decade lineability/spaceability has been investigated in rather general settings; for instance, Set Theory, Probability Theory, Functional Analysis, Measure Theory, etc. It is a common feeling that positive results on lineability/spaceability are quite natural (i.e., in general “large” subspaces can be found inside exotic subsets of vector spaces, in quite different settings) and more restrictive approaches have been attempted. In this paper we introduce and explore a new approach in this direction.

ABSTRACT For we prove that there is a -dimensional subspace of such that, except for the null vector, all of its vectors fail to be absolutely (r, s)-summing regardless of the real numbers r, s, with . This extends a result proved by Maddox in 1987. Moreover, the result is sharp in the sense that it is not valid for

In the short note we prove that for every $0

The notion of multipolynomials was recently introduced and explored by T. Velanga in [10] as an attempt to encompass the theories of polynomials and multi- linear operators. In the present paper we push this subject further, by proving Hardy- Littlewood inequalities for multipolynomials and, en passant, a variant of the Kahane- Salem-Zygmund inequality in this framework.