Infinite pointwise lineability: general criteria and applications

Abstract

In this paper we introduce the concept of infinite pointwise dense lineability (spaceability), and provide a criterion to obtain density from mere lineability. As an application, we study the linear and topological structures within the set of infinite differentiable and integrable functions, for any order $p\ge 1$, on ${\mathbb{R}}^N$ which are unbounded in a prefixed set.

References in corpus (1)

• Dense lineability and spaceability in certain subsets of ${\ell }_{\infty }$

Cited by in corpus (2)

• Modes of convergence of sequences of holomorphic functions: a linear point of view
• Hypercyclic subspaces for sequences of finite order differential operators