Derivations from Banach function algebras

Dales, H.G. and White, K. A. L. (2004) Derivations from Banach function algebras. The Quarterly Journal of Mathematics, 55 (4). pp. 451-461. ISSN 0033-5606

Abstract

We study the structure of derivations D : AlgA C [X] → A, where A is a function algebra defined on a compact subset of C such that A contains C [X]. We show that, under certain conditions on the algebra A, all such derivations are zero. We give examples to show the necessity of these conditions.