A multiplier algebra functional calculus
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- by Kelly Bickel, Michael Hartz and John E. McCarthy PDF
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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 $\mathbb {C}^d$.References
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Additional Information
- Kelly Bickel
- Affiliation: Department of Mathematics, Bucknell University, 701 Moore Ave, Lewisburg, Pennsylvania 17837
- MR Author ID: 997443
- Email: kelly.bickel@bucknell.edu
- Michael Hartz
- Affiliation: Department of Mathematics, Washington University in St. Louis, One Brookings Drive, St. Louis, Missouri 63130
- MR Author ID: 997298
- Email: mphartz@wustl.edu
- John E. McCarthy
- Affiliation: Department of Mathematics, Washington University in St. Louis, One Brookings Drive, St. Louis, Missouri 63130
- MR Author ID: 271733
- ORCID: 0000-0003-0036-7606
- Email: mccarthy@wustl.edu
- 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 - © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 370 (2018), 8467-8482
- MSC (2010): Primary 47A60; Secondary 47A13, 46E22
- DOI: https://doi.org/10.1090/tran/7381
- MathSciNet review: 3864384