%0 Journal Article
%A Enflo, Per H.
%A Gurariy, Vladimir
%A Seoane Sepúlveda, Juan Benigno
%T Some results and open questions on spaceability in function spaces
%D 2014
%@ 0002-9947
%U https://hdl.handle.net/20.500.14352/33431
%X A subset M of a topological vector space X is called lineable (respectively, spaceable) in X if there exists an infinite dimensional linear space (respectively, an infinite dimensional closed linear space) Y subset of M boolean OR {0}. In this article we prove that, for every infinite dimensional closed subspace X of C[0, 1], the set of functions in X having infinitely many zeros in [0, 1] is spaceable in X. We discuss problems related to these concepts for certain subsets of some important classes of Banach spaces (such as C[0, 1] or Muntz spaces). We also propose several open questions in the field and study the properties of a new concept that we call the oscillating spectrum of subspaces of C[0, 1], as well as oscillating and annulling properties of subspaces of C[0, 1].
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