$L_{p}[0,1] \setminus \bigcup\limits_{q>p} L_{q}[0,1]$ is spaceable for every $p>0$
| Autor: | Botelho, G., Fávaro, V. V., Pellegrino, D., Seoane-Sepúlveda, J. B. |
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| Rok vydání: | 2011 |
| Předmět: | |
| Zdroj: | Linear Algebra and its Applications 436 (2012) 2963-2965 |
| Druh dokumentu: | Working Paper |
| Popis: | In this short note we prove the result stated in the title; that is, for every $p>0$ there exists an infinite dimensional closed linear subspace of $L_{p}[0,1]$ every nonzero element of which does not belong to $\bigcup\limits_{q>p} L_{q}[0,1]$. 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. Comment: 3 pages |
| Databáze: | arXiv |
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