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Some results and open questions on spaceability in function spaces

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Enflo, Per H. and Gurariy, Vladimir and Seoane-Sepúlveda, Juan B. (2014) Some results and open questions on spaceability in function spaces. Transactions of the American Mathematical Society, 336 . pp. 611-625. ISSN 0002-9947

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Official URL: http://www.ams.org/journals/tran/2014-366-02/S0002-9947-2013-05747-9/S0002-9947-2013-05747-9.pdf


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Abstract

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].


Item Type:Article
Uncontrolled Keywords:Lineability; spaceability; subspaces of continuous functions; zeros of functions; Muntz spaces
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:24145
Deposited On:09 Jan 2014 12:16
Last Modified:28 Nov 2016 09:25

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