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

## TL;DR

This paper demonstrates that in certain quasi-Banach sequence spaces, there exists an infinite-dimensional subspace of bounded linear operators where every nonzero operator is non-absolutely summing, revealing a rich structure of such operators.

## Contribution

It establishes the spaceability of non-absolutely summing operators in $ ext{L}( extstyle ext{ell}_p; ext{ell}_p)$ for $0<p<1$, improving previous results.

## Key findings

- Existence of infinite-dimensional subspace of non-absolutely summing operators.
- Every nonzero operator in this subspace is non $(r,s)$-absolutely summing.
- The result applies for all $0<p<1$ and $1 extless s extless r< extless \infty$.

## 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 $1\leq s\leq r<\infty$. This improve a result obtained in \cite{DanielT}.