Non-reflexivity of the derivation space from Banach algebras of analytic functions

Abstract

Abstract. Let Ω be an open connected subset of the plane, and let A be a Banach algebra of analytic functions on Ω. We show that the space of bounded derivations from A into A * is not reflexive. We also obtain similar results when A = C (n) [0, 1] for n ≥ 2.