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L-p[0,1] \ boolean OR(q > p) L-q[0,1] is spaceable for every p > 0

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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
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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