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arXiv · 1302.2275

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.

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Lior Fishman, David S. Simmons, Mariusz Urbański. 2013-02-09. Diophantine approximation in Banach spaces. https://arxiv.org/abs/1302.2275

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