Diophantine approximation in Banach spaces
Journal de théorie des nombres de Bordeaux, Volume 26 (2014) no. 2, pp. 363-384.

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.

Dans cet article, nous étendons à la dimension infinie la théorie de l’approximation diophantienne simultanée. De plus, nous discutons des théorèmes de type Dirichlet dans un cadre très général et nous définissons ce que signifie étre optimal pour un tel théorème. Nous montrons que l’optimalité est impliquée par, mais n’implique pas, l’existence de points mal approchables.

DOI: 10.5802/jtnb.871
Lior Fishman 1; David Simmons 2; Mariusz Urbański 1

1 University of North Texas Department of Mathematics 1155 Union Circle #311430 Denton, TX 76203-5017, USA
2 Ohio State University Department of Mathematics 231 W. 18th Avenue Columbus Ohio, OH 43210-1174, USA
     author = {Lior Fishman and David Simmons and Mariusz Urba\'nski},
     title = {Diophantine approximation in {Banach} spaces},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {363--384},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {26},
     number = {2},
     year = {2014},
     doi = {10.5802/jtnb.871},
     mrnumber = {3320484},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.871/}
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Lior Fishman; David Simmons; Mariusz Urbański. Diophantine approximation in Banach spaces. Journal de théorie des nombres de Bordeaux, Volume 26 (2014) no. 2, pp. 363-384. doi : 10.5802/jtnb.871. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.871/

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