Universal series in ∩ p >1 ℓ p

In this paper an abstract condition is given yielding universal series defined by sequences a ={ a j }j = 1 ∞in ∩ p >1 ℓ p but not in ℓ 1 . We obtain a unification of some known results related to approximation by translates of specific functions including the Riemann ζ‐function, or a fundamental solution of a given elliptic operator in ℝ ν with constant coefficients or an approximate identity as, for example, the normal distribution. Another application gives universal trigonometric series in ℝ ν simultaneously with respect to all σ‐finite Borel measures in ℝ ν . Stronger results are obtained by using universal Dirichlet series.