Embedding the weighted space Hv0(G, E) of holomorphic functions into the sequence space c0(E)

We embed almost isometrically the generalized weighted space Hv(0)(G, E) of holomorphic functions on an open subset G of C-N with values in a Banach space E, into c(0)(E), the space of all null sequences in E, where v is an operator-valued continuous function on G vanishing nowhere. This extends and generalizes some known results in the literature. We then deduce the non 1-Hyers-Rassias stability of the isometry functional equation in the framework of Banach spaces.