The Berezin symbol and multipliers of functional Hilbert spaces
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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.References
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Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 3687-3691
- MSC: Primary 46E22; Secondary 47B99
- DOI: https://doi.org/10.1090/S0002-9939-1995-1277120-3
- MathSciNet review: 1277120