Universal series in ∧p>1lp

In this paper an abstract condition is given yielding universal series defined by sequences a = {a(j)}infinity j=1 in boolean AND(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 zeta-function, or a fundamental solution of a given elliptic operator in R-nu with constant coefficients or an approximate identity as, for example, the normal distribution. Another application gives universal trigonometric series in R-nu simultaneously with respect to all sigma-finite Borel measures in R-nu. Stronger results are obtained by using universal Dirichlet series.