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Nonlinear subsets of function spaces and spaceability

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Ruiz Bermejo, César and Sánchez de los Reyes, Víctor Manuel (2014) Nonlinear subsets of function spaces and spaceability. Linear algebra and its applications (463). pp. 56-67. ISSN 0024-3795

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Official URL: http://www.sciencedirect.com/science/article/pii/S0024379514005904




Abstract

In this paper, we study the existence of infinite dimensional closed linear subspaces of a rearrangement invariant space on [0,1] every nonzero element of which does not belong to any included rearrangement invariant space of the same class such that the inclusion operator is disjointly strictly singular. We consider Lorentz, Marcinkiewicz and Orlicz spaces. The answer is affirmative for Marcinkiewicz spaces and negative for Lorentz and Orlicz spaces. Also, the same problem is studied for Nakano spaces assuming different hypothesis


Item Type:Article
Uncontrolled Keywords:Spaceability; Lorentz space; Marcinkiewicz space; Orlicz space; Nakano space; Disjointly strictly singular
Subjects:Sciences > Mathematics
ID Code:28994
Deposited On:04 Mar 2015 10:30
Last Modified:25 Aug 2015 08:06

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