On the complexity of Hamel bases of infinite-dimensional Banach spaces

DOI10.4064/CM89-1-9zbMATH Open0998.46008arXivmath/0109177OpenAlexW2051178236MaRDI QIDQ2717746

Lorenz Halbeisen

Publication date: 17 June 2001

Published in: Colloquium Mathematicum (Search for Journal in Brave)

Abstract: We call a subset S of a topological vector space V linearly Borel, if for every finite number n, the set of all linear combinations of S of length n is a Borel subset of V. It will be shown that a Hamel base of an infinite dimensional Banach space can never be linearly Borel. This answers a question of Anatolij Plichko.

Full work available at URL: https://arxiv.org/abs/math/0109177

zbMATH Keywords

Banach spaceHamel basisBorel setBaire categoryBaire property

Mathematics Subject Classification ID

Baire category, Baire spaces (54E52) Geometry and structure of normed linear spaces (46B20) Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces (46B15)

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