Diophantine approximation in Banach spaces
classification
🧮 math.NT
keywords
approximationdiophantineapproximablebadlybanachdefinedimensionsdirichlet-type
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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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