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Botelho, G. and Fávaro, V.V. and Pellegrino, Daniel and Seoane-Sepúlveda, Juan B.
(2012)
*L-p[0,1] \ boolean OR(q > p) L-q[0,1] is spaceable for every p > 0.*
Linear Algebra and its Applications, 436
(9).
pp. 2963-2965.
ISSN 0024-3795

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Official URL: http://www.elsevier.com/locate/laa

## Abstract

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 sub-space of L-p[0, 1] every nonzero element of which does not belong to boolean OR(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 Botelho et al. (2011) [3] for subsets of sequence spaces. (C) 2012 Elsevier Inc. All rights reserved.

Item Type: | Article |
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Uncontrolled Keywords: | Lineability; Spaceability; Lp spaces; Quasi-Banach spaces |

Subjects: | Sciences > Mathematics > Functional analysis and Operator theory |

ID Code: | 19973 |

Deposited On: | 15 Feb 2013 17:24 |

Last Modified: | 25 Nov 2016 12:41 |

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