Nonlinear subsets of function spaces and spaceability
Functional Analysis
2014-09-04 v5
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.
Cite
@article{arxiv.1401.5906,
title = {Nonlinear subsets of function spaces and spaceability},
author = {César Ruiz and Víctor M. Sánchez},
journal= {arXiv preprint arXiv:1401.5906},
year = {2014}
}
Comments
12 pages. arXiv admin note: text overlap with arXiv:1204.2170 by other authors