مشخصات پژوهش

Let G be a locally compact group, be a Young function and ω be a weight on G. An associated weighted Orlicz space is denoted by L(G, ω). For any S ⊆ G, a family of left translations {Ls}s∈S on L(G, ω), defined by Ls f (t) := f (s−1t) for all t ∈ G, is said S-universal if there exists a function f ∈ L(G, ω), called an S-universal vector, such that its S-orbit, namely, OrbS( f ) = {Ls( f ) : s ∈ S} is dense in L(G, ω). In this paper, first it is shown that any compact group G, does not admit an S-universal vector in L(G, ω) and only the infinite dimensional weighted Orlicz spaces L(G, ω) may contain it. In the sequel, under natural restrictions, the existence of S-universal vector leads to find out that G must be second countable. Moreover, we give a necessary and sufficient condition for {Ls}s∈S to be S-universal on L(G, ω). At last, some other sp