Nonlinear subsets of function spaces and spaceability

作者：Ruiz Cesar; Sanchez Victor M^*

来源：Linear Algebra and Its Applications, 2014, 463: 56-67.

DOI：10.1016/j.laa.2014.09.005

• Spaceability
• Lorentz space
• Marcinkiewicz space
• Orlicz space
• Nakano space
• Disjointly strictly singular

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.

• 出版日期2014-12-15