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).