Spaceability of the set of bounded linear non-absolutely summing operators in Quasi-Banach sequence spaces

Abstract

In the short note we prove that for every $0<p<1$, there exists an infinite dimensional closed linear subspace of $\mathcal{L}\left({\ell }_p;{\ell }_p\right)$ every nonzero element of which is non $(r,s)$-absolutely summing operator for the real numbers $r,s$ with $1\le s\le r<\infty$. This improve a result obtained in \cite{DanielT}.

5 pages