Diophantine approximation in Banach spaces
Number Theory
2016-02-29 v5
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.
Cite
@article{arxiv.1302.2275,
title = {Diophantine approximation in Banach spaces},
author = {Lior Fishman and David S. Simmons and Mariusz Urbański},
journal= {arXiv preprint arXiv:1302.2275},
year = {2016}
}