Γ-supercyclicity of families of translates in weighted Lp-spaces on locally compact groups

Let omega be a weight function defined on a locally compact group G, 1 <= p < +infinity, S subset of G and let us assume that for any s is an element of S, the left translation operator T-s is continuous from the weighted L-p-space L-p(G, omega) into itself. For a given set Gamma subset of C, a vector f is an element of L-p(G, omega) is said to be (Gamma, S)-dense if the set {lambda T(s)f : lambda is an element of Gamma, s is an element of S} is dense in L-p(G, omega). In this paper, we characterize the existence of (Gamma, S)-dense vectors in L-p(G, omega) in terms of the weight and the set Gamma. (C) 2020 Elsevier Inc. All rights reserved.