Diophantine approximation in Banach spaces

Lior Fishman, David S. Simmons, Mariusz Urbański

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Abstract

In this paper, we extend the theory of simultaneous Diophantine approximation to infinite dimensions. Moreover, we discuss Dirichlet-type theorems in a very general framework and define what it means for such a theorem to be optimal. We show that optimality is implied by but does not imply the existence of badly approximable points.
Original languageEnglish
Pages (from-to)363-384
Number of pages22
JournalJournal de Théorie des Nombres de Bordeaux
Volume26
Issue number2
Publication statusPublished - 2014

Bibliographical note

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Keywords

  • math.NT

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