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Bohr's strip for vector valued Dirichlet series


Defant, Andreas and García, Domingo and Maestre, Manuel and Pérez García, David (2008) Bohr's strip for vector valued Dirichlet series. Mathematische Annalen, 342 (3). pp. 533-555. ISSN 0025-5831

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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.

Item Type:Article
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:17787

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