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arXiv · 0909.1867

Characterising derivations from the disc algebra to its dual

Yemon Choi·Matthew J. Heath
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Abstract

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.

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BibTeXRIS

Yemon Choi, Matthew J. Heath. 2009-09-10. Characterising derivations from the disc algebra to its dual. https://doi.org/10.1090/s0002-9939-2010-10520-8

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