$L_{p}[0,1] \setminus \bigcup\limits_{q>p} L_{q}[0,1]$ is spaceable for every $p>0$
Functional Analysis
2012-08-30 v1
Abstract
In this short note we prove the result stated in the title; that is, for every there exists an infinite dimensional closed linear subspace of every nonzero element of which does not belong to . This answers in the positive a question raised in 2010 by R. M. Aron on the spaceability of the above sets (for both, the Banach and quasi-Banach cases). We also complete some recent results from \cite{BDFP} for subsets of sequence spaces.
Keywords
Cite
@article{arxiv.1106.0309,
title = {$L_{p}[0,1] \setminus \bigcup\limits_{q>p} L_{q}[0,1]$ is spaceable for every $p>0$},
author = {G. Botelho and V. V. Fávaro and D. Pellegrino and J. B. Seoane-Sepúlveda},
journal= {arXiv preprint arXiv:1106.0309},
year = {2012}
}
Comments
3 pages