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Multipliers and
operator space structure of weak product spaces
Raphaël Clouâtre and Michael Hartz |
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Vol. 14 (2021), No. 6, 1905–1924
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Abstract |
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In the theory of reproducing kernel Hilbert spaces, weak product spaces generalize the notion of the Hardy space . For complete Nevanlinna–Pick spaces , we characterize all multipliers of the weak product space . In particular, we show that if has the so-called column-row property, then the multipliers of and of coincide. This result applies in particular to the classical Dirichlet space and to the Drury–Arveson space on a finite-dimensional ball. As a key device, we exhibit a natural operator space structure on , which enables the use of dilations of completely bounded maps. |
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Keywords
complete Nevanlinna–Pick space, weak product, multiplier,
Hankel operator, completely bounded map, dilation
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Mathematical Subject Classification 2010
Primary: 46E22
Secondary: 46L07, 47A20
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Milestones
Received: 27 September 2019
Revised: 10 January 2020
Accepted: 3 March 2020
Published: 7 September 2021
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Authors |
| Raphaël Clouâtre | |
| Department of Mathematics University of Manitoba Winnipeg, MB Canada |
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| Michael Hartz | |
| Fachrichtung Mathematik Universität des Saarlandes Saarbrücken Germany |
Fakultät für Mathematik und
Informatik FernUniversität in Hagen Hagen Germany |
