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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



The Berezin symbol and multipliers of functional Hilbert spaces

Author: Semra Kiliç
Journal: Proc. Amer. Math. Soc. 123 (1995), 3687-3691
MSC: Primary 46E22; Secondary 47B99
MathSciNet review: 1277120
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Abstract: This paper focuses on a multiplicative property of the Berezin symbol $ \tilde A$, of a given linear map $ A:\mathcal{H} \mapsto \mathcal{H}$, where $ \mathcal{H}$ is a functional Hilbert space of analytic functions. We show $ \widetilde{AB} = \tilde A\tilde B$ for all B in $ \mathcal{B}(\mathcal{H})$ if and only if A is a multiplication operator $ {M_\varphi }$, where $ \varphi $ is a multiplier. We also present a version of this result for vector-valued functional Hilbert spaces.

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Keywords: Berezin symbol, multiplier, functional Hilbert spaces, multiplication operators, Toeplitz operators
Article copyright: © Copyright 1995 American Mathematical Society

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