This is an announcement for the paper "Nonlinear subsets of functions spaces and spaceability" by Cesar Ruiz and Victor M. Sanchez.

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.

Archive classification: math.FA

Mathematics Subject Classification: 46E30

Remarks: 11 pages

Submitted from: victorms@mat.ucm.es

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1401.5906

or

http://arXiv.org/abs/1401.5906