Characterizing derivations from the disk algebra to its dual

Authors:
Y. Choi and M. J. Heath

Journal:
Proc. Amer. Math. Soc. **139** (2011), 1073-1080

MSC (2010):
Primary 46J15; Secondary 30H10, 47B47

Published electronically:
August 3, 2010

MathSciNet review:
2745657

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Abstract: We show that the space of all bounded derivations from the disk algebra into its dual can be identified with the Hardy space ; using this, we infer that all such derivations are compact. Also, given a fixed derivation , we construct a finite, positive Borel measure on the closed disk, such that factors through . Such a measure is known to exist, for any bounded linear map from the disk algebra to its dual, by results of Bourgain and Pietsch, but these results are highly non-constructive.

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Additional Information

**Y. Choi**

Affiliation:
Département de mathématiques et de statistique, Pavillon Alexandre-Vachon, Université Laval, Québec, QC, Canada, G1V 0A6

Address at time of publication:
Department of Mathematics and Statistics, McLean Hall, University of Saskatchewan, 106 Wiggins Road, Saskatoon, SK, Canada S7N 5E6

Email:
y.choi.97@cantab.net

**M. J. Heath**

Affiliation:
Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal

Email:
mheath@math.ist.utl.pt

DOI:
http://dx.doi.org/10.1090/S0002-9939-2010-10520-8

Keywords:
Derivation,
disk algebra,
Hardy space

Received by editor(s):
December 15, 2009

Received by editor(s) in revised form:
March 30, 2010

Published electronically:
August 3, 2010

Additional Notes:
The second author was supported by post-doctoral grant SFRH/BPD/40762/2007 from FCT (Portugal).

Communicated by:
Nigel J. Kalton

Article copyright:
© Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.