Defant, AndreasGarcía, DomingoMaestre, ManuelPérez García, David2023-06-202023-06-2020080025-583110.1007/s00208-008-0246-zhttps://hdl.handle.net/20.500.14352/50304Bohr showed that the width of the strip (in the complex plane) on which a given Dirichlet series Sigma a(n)/n(s), s is an element of C, converges uniformly but not absolutely, is at most 1/2, and Bohnenblust-Hille that this bound in general is optimal. We prove that for a given infinite dimensional Banach space Y the width of Bohr's strip for a Dirichlet series with coefficients a(n) in Y is bounded by 1 - 1/Cot (Y), where Cot (Y) denotes the optimal cotype of Y. This estimate even turns out to be optimal, and hence leads to a new characterization of cotype in terms of vector valued Dirichlet series.engjournal articlehttp://www.springerlink.com/content/a3k0122058uw8228/fulltext.pdfhttp://www.springerlink.com/restricted access517.98Análisis funcional y teoría de operadores