A note on weighted Banach spaces of holomorphic functions

Abstract.

For every open subset G of $\mathbb{C}^N$ and for every continuous, strictly positive weight v on G, the Banach space of all the holomorphic functions f on G such that $v|f|$ vanishes at infinity on G, endowed with the natural weighted sup-norm, is isomorphic to a closed subspace of the Banach space c ₀; hence it is reflexive if and only if it is finite dimensional.