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oai:docta.ucm.es:20.500.14352/334312025-04-08T14:25:30Zcom_20.500.14352_14col_20.500.14352_15

Enflo, Per H. Gurariy, Vladimir Seoane Sepúlveda, Juan Benigno 2023-06-19T13:22:47Z 2023-06-19T13:22:47Z 2014 0002-9947 10.1090/S0002-9947-2013-05747-9 https://hdl.handle.net/20.500.14352/33431 http://www.ams.org/journals/tran/2014-366-02/S0002-9947-2013-05747-9/S0002-9947-2013-05747-9.pdf http://www.ams.org/ 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]. eng restricted access Some results and open questions on spaceability in function spaces journal article