%0 Journal Article
%T Characterising derivations from the disc algebra to its dual
%A Yemon Choi
%A Matthew J. Heath
%J Mathematics
%D 2009
%I arXiv
%R 10.1090/S0002-9939-2010-10520-8
%X We show that the space of all bounded derivations from the disc algebra into its dual can be identified with the Hardy space $H^1$; using this, we infer that all such derivations are compact. Also, given a fixed derivation $D$, we construct a finite, positive Borel measure $\mu_D$ on the closed disc, such that $D$ factors through $L^2(\mu_D)$. Such a measure is known to exist, for any bounded linear map from the disc algebra to its dual, by results of Bourgain and Pietsch, but these results are highly non-constructive.
%U http://arxiv.org/abs/0909.1867v2