1. bookVolumen 17 (2022): Heft 1 (December 2022)
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Zeitschrift
eISSN
2309-5377
Erstveröffentlichung
30 Dec 2013
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2 Hefte pro Jahr
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Englisch
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On Some Properties of Irrational Subspaces

Online veröffentlicht: 31 May 2022
Volumen & Heft: Volumen 17 (2022) - Heft 1 (December 2022)
Seitenbereich: 89 - 104
Eingereicht: 23 Jul 2021
Akzeptiert: 26 Jan 2022
Zeitschriftendaten
License
Format
Zeitschrift
eISSN
2309-5377
Erstveröffentlichung
30 Dec 2013
Erscheinungsweise
2 Hefte pro Jahr
Sprachen
Englisch
Abstract

In this paper, we discuss some properties of completely irrational subspaces. We prove that there exist completely irrational subspaces that are badly approximable and, moreover, sets of such subspaces are winning in different senses. We get some bounds for Diophantine exponents of vectors that lie in badly approximable subspaces that are completely irrational; in particular, for any vector ξ from two-dimensional badly approximable completely irrational subspace of ℝd one has ω(ξ)5-12 \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over \omega } \left( \xi \right) \le {{\sqrt {5 - 1} } \over 2} . Besides that, some statements about the dimension of subspaces generated by best approximations to completely irrational subspace easily follow from properties that we discuss.

MSC 2010

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