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arXiv · 1812.03951

Random unconditional convergence of vector-valued Dirichlet series

Daniel Carando·Felipe Marceca·Melisa Scotti·Pedro Tradacete
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Abstract

We study random unconditionality of Dirichlet series in vector-valued Hardy spaces $\mathcal H_p(X)$. It is shown that a Banach space $X$ has type 2 (respectively, cotype 2) if and only if for every choice $(x_n)_n\subset X$ it follows that $(x_n n^{-s})_n$ is Random unconditionally convergent (respectively, divergent) in $\mathcal H_2(X)$. The analogous question on $\mathcal H_p(X)$ spaces for $p\neq2$ is also explored. We also provide explicit examples exhibiting the differences between the unconditionality of $(x_n n^{-s})_n$ in $\mathcal H_p(X)$ and that of $(x_n z^n)_n$ in $H_p(X)$.

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Daniel Carando, Felipe Marceca, Melisa Scotti, Pedro Tradacete. 2018-12-10. Random unconditional convergence of vector-valued Dirichlet series. https://arxiv.org/abs/1812.03951

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