This is an announcement for the paper "Lineability criteria, with applications" by Luis Bernal-Gonzalez and Manuel Ordonez-Cabrera.
Abstract: Lineability is a property enjoyed by some subsets within a vector space X. A subset A of X is called lineable whenever A contains, except for zero, an infinite dimensional vector subspace. If, additionally, X is endowed with richer structures, then the more stringent notions of dense-lineability, maximal dense-lineability and spaceability arise naturally. In this paper, several lineability criteria are provided and applied to specific topological vector spaces, mainly function spaces. Sometimes, such criteria furnish unified proofs of a number of scattered results in the related literature. Families of strict-order integrable functions, hypercyclic vectors, non-extendable holomorphic mappings, Riemann non-Lebesgue integrable functions, sequences not satisfying the Lebesgue dominated convergence theorem, nowhere analytic functions, bounded variation functions, entire functions with fast growth and Peano curves, among others, are analyzed from the point of view of lineability.
Archive classification: math.FA
Mathematics Subject Classification: 15A03, 26A46, 28A25, 30B40, 46E10, 46E30, 47A16
Remarks: 38 pages
Submitted from: lbernal@us.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1309.3656
or