Random unconditional convergence of vector-valued Dirichlet series

CARANDO, DANIEL; MARCECA, FELIPE; SCOTTI, MELISA; TRADACETE, PEDRO

JOURNAL OF FUNCTIONAL ANALYSIS

ACADEMIC PRESS INC ELSEVIER SCIENCE

Año: 2019 vol. 277 p. 3156 - 3178

0022-1236

We study random unconditionality of Dirichlet series in vector-valued Hardy spaces Hp(X). It is shown that a Banach space X has type 2 (respectively, cotype 2) if and only if for every choice (xn)n⊂X it follows that (xnn−s)n is random unconditionally convergent (respectively, divergent) in H2(X). The analogous question on Hp(X) spaces for p≠2 is also explored. We also provide explicit examples exhibiting the differences between the unconditionality of (xnn−s)n in Hp(X) and that of (xnzn)n in Hp(X).