Publication: Bohr's strip for vector valued Dirichlet series
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2008
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Springer
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Bohr 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.
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