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Transactions of the American Mathematical Society

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A multiplier algebra functional calculus


Authors: Kelly Bickel, Michael Hartz and John E. McCarthy
Journal: Trans. Amer. Math. Soc. 370 (2018), 8467-8482
MSC (2010): Primary 47A60; Secondary 47A13, 46E22
DOI: https://doi.org/10.1090/tran/7381
Published electronically: June 26, 2018
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Abstract: This paper generalizes the classical Sz.-Nagy-Foias $ H^{\infty }(\mathbb{D})$ functional calculus for Hilbert space contractions. In particular, we replace the single contraction $ T$ with a tuple $ T=(T_1, \dots , T_d)$ of commuting bounded operators on a Hilbert space and replace $ H^{\infty }(\mathbb{D})$ with a large class of multiplier algebras of Hilbert function spaces on the unit ball in $ \mathbb{C}^d$.


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Additional Information

Kelly Bickel
Affiliation: Department of Mathematics, Bucknell University, 701 Moore Ave, Lewisburg, Pennsylvania 17837
Email: kelly.bickel@bucknell.edu

Michael Hartz
Affiliation: Department of Mathematics, Washington University in St. Louis, One Brookings Drive, St. Louis, Missouri 63130
Email: mphartz@wustl.edu

John E. McCarthy
Affiliation: Department of Mathematics, Washington University in St. Louis, One Brookings Drive, St. Louis, Missouri 63130
Email: mccarthy@wustl.edu

DOI: https://doi.org/10.1090/tran/7381
Keywords: Functional calculus, multiplier algebra, unit ball
Received by editor(s): March 28, 2017
Published electronically: June 26, 2018
Additional Notes: The first author was partially supported by National Science Foundation Grant DMS 1448846
The second author was partially supported by a Feodor Lynen Fellowship
The third author was partially supported by National Science Foundation Grant DMS 1565243
Article copyright: © Copyright 2018 American Mathematical Society

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