Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Toeplitz operators and localization operators

Author: Miroslav Englis
Journal: Trans. Amer. Math. Soc. 361 (2009), 1039-1052
MSC (2000): Primary 47B35; Secondary 42C40, 32M15, 81R30
Published electronically: August 18, 2008
MathSciNet review: 2452833
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Abstract: We show that for any localization operator on the Fock space with polynomial window, there exists a constant coefficient linear partial differential operator $ D$ such that the localization operator with symbol $ f$ coincides with the Toeplitz operator with symbol $ Df$. An analogous result also holds in the context of Bergman spaces on bounded symmetric domains. This verifies a recent conjecture of Coburn and simplifies and generalizes recent results of Lo.

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Miroslav Englis
Affiliation: Mathematics Institute, Silesian University at Opava, Na Rybníčku 1, 74601 Opava, Czech Republic – and – Mathematics Institute, Žitná 25, 11567 Prague 1, Czech Republic

Keywords: Toeplitz operator, localization operator, bounded symmetric domain, Segal-Bargmann space, Bergman space
Received by editor(s): July 31, 2006
Received by editor(s) in revised form: May 7, 2007
Published electronically: August 18, 2008
Additional Notes: This research was supported by GA ČR grant no. 201/06/0128 and Ministry of Education research plan no. MSM4781305904.
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.