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Characterizing derivations from the disk algebra to its dual

Research output: Contribution to Journal/Magazine › Journal article › peer-review

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Characterizing derivations from the disk algebra to its dual. / Choi, Yemon; Heath, Matthew J.
In: Proceedings of the American Mathematical Society, Vol. 139, No. 3, 03.08.2011, p. 1073-1080.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Choi, Y & Heath, MJ 2011, 'Characterizing derivations from the disk algebra to its dual', Proceedings of the American Mathematical Society, vol. 139, no. 3, pp. 1073-1080. https://doi.org/10.1090/S0002-9939-2010-10520-8

APA

Choi, Y., & Heath, M. J. (2011). Characterizing derivations from the disk algebra to its dual. Proceedings of the American Mathematical Society, 139(3), 1073-1080. https://doi.org/10.1090/S0002-9939-2010-10520-8

Vancouver

Choi Y, Heath MJ. Characterizing derivations from the disk algebra to its dual. Proceedings of the American Mathematical Society. 2011 Aug 3;139(3):1073-1080. doi: 10.1090/S0002-9939-2010-10520-8

Author

Choi, Yemon ; Heath, Matthew J. / Characterizing derivations from the disk algebra to its dual. In: Proceedings of the American Mathematical Society. 2011 ; Vol. 139, No. 3. pp. 1073-1080.

Bibtex

@article{947bf432463b46e297c30b35367bd5a7,
title = "Characterizing derivations from the disk algebra to its dual",
abstract = "We show that the space of all bounded derivations from the disk 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 disk, such that $ D$ factors through $ L^2(\mu_D)$. 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. ",
author = "Yemon Choi and Heath, {Matthew J.}",
year = "2011",
month = aug,
day = "3",
doi = "10.1090/S0002-9939-2010-10520-8",
language = "English",
volume = "139",
pages = "1073--1080",
journal = "Proceedings of the American Mathematical Society",
issn = "0002-9939",
publisher = "American Mathematical Society",
number = "3",

}

RIS

TY - JOUR

T1 - Characterizing derivations from the disk algebra to its dual

AU - Choi, Yemon

AU - Heath, Matthew J.

PY - 2011/8/3

Y1 - 2011/8/3

N2 - We show that the space of all bounded derivations from the disk 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 disk, such that $ D$ factors through $ L^2(\mu_D)$. 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.

AB - We show that the space of all bounded derivations from the disk 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 disk, such that $ D$ factors through $ L^2(\mu_D)$. 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.

U2 - 10.1090/S0002-9939-2010-10520-8

DO - 10.1090/S0002-9939-2010-10520-8

M3 - Journal article

VL - 139

SP - 1073

EP - 1080

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 3

ER -