Some remarks on abstract Universal series

We introduce a new class of Universal series, in the abstract setting. This class lies between two already known classes of Universal series. By two examples we differentiate these classes. These examples are the first examples in the case where all classes are non-void. We also prove that the class of Universal series where the approximating indexes have upper density 1 is dense and G δ and that the class of lower frequently universal series is of the first category.