Algebras and Banach spaces of Dirichlet series with maximal Bohr's strip.

We study linear and algebraic structures in sets of Dirichlet series with maximal Bohr's strip. More precisely, we consider a set M of Dirichlet series which are uniformly continuous on the right half plane and whose strip of uniform but not absolute convergence has maximal width, i.e., 1 2 . Considering the uniform norm, we show that M contains an isometric copy of ℓ 1 (except zero) and is strongly ℵ 0 -algebrable. Also, there is a dense G δ set such that any of its elements generates a free algebra contained in M ∪ { 0 } . Furthermore, we investigate M as a subset of the Hilbert space of Dirichlet series whose coefficients are square-summable. In this case, we prove that M contains an isometric copy of ℓ 2 (except zero). [ABSTRACT FROM AUTHOR]