Let GLn be a complex general linear group. In this paper we determine the structure of all Jordan triple product maps from GL1 to GLm for m = 2, 3. The results are applied to determine the structure of all continuous Jordan triple product maps betweenGL1 andGLm for m = 2, 3. These are the continuous maps ϕ : GL1 → GLm which satisfy ϕ(zwz) = ϕ(z)ϕ(w)ϕ(z), z,w ∈ GL1.
