arXiv subjects

César Ruiz

Publications and source records attributed to César Ruiz.

3 recordsLinked to original sources

arXiv2024

Disjointly strictly singular inclusions between variable Lebesgue spaces

Disjointly strictly singular inclusions between variable Lebesgue spaces $L^{p(\cdot)}(μ)$ on finite measure are characterized. Suitable criteria in terms of the (bounded or unbounded) exponents are given. It is proved the equivalence of $L$-weak compactness (also called almost compactness) and disjoint strict singularity for variable Lebesgue space inclusions. For infinite measure any inclusion $L^{p(\cdot)}(μ) \hookrightarrow L^{q(\cdot)}(μ)$ is not disjointly strictly singular. No restrictions on the exponent are imposed.

math.FA↗

arXiv2019

On the structure of variable exponent spaces

The first part of this paper surveys several results on the lattice structure of variable exponent Lebesgue function spaces (or Nakano spaces) $\lpv$. In the second part strictly singular and disjointly strictly singular operators between spaces $\lpv$ are studied. New results on the disjoint strict singularity of the inclusions $ L^{p(\cdot)}(Ω) \hookrightarrow L^{q(\cdot)}(Ω)$ are given.

math.FA↗

arXiv2014

Nonlinear subsets of function spaces and spaceability

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.

math.FA↗