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arXiv · 1902.09668

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

Daniel Tomaz
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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}.

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Daniel Tomaz. 2019-02-25. Spaceability of the set of bounded linear non-absolutely summing operators in Quasi-Banach sequence spaces. https://arxiv.org/abs/1902.09668

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