Kiliç, Semra The Berezin symbol and multipliers of functional Hilbert spaces. (English) Zbl 0847.46010 Proc. Am. Math. Soc. 123, No. 12, 3687-3691 (1995). Summary: This paper focuses on a multiplicative property of the Berezin symbol \(\widetilde A\), of a given linear map \(A: {\mathcal H}\mapsto {\mathcal H}\), where \(\mathcal H\) is a functional Hilbert space of analytic functions. We show \(\widetilde{AB}= \widetilde A\widetilde B\) 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. Cited in 11 Documents MSC: 46E22 Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) 47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators 47B38 Linear operators on function spaces (general) Keywords:multiplication operators; Toeplitz operators; multiplicative property; Berezin symbol; functional Hilbert space of analytic functions; vector-valued functional Hilbert spaces PDFBibTeX XMLCite \textit{S. Kiliç}, Proc. Am. Math. Soc. 123, No. 12, 3687--3691 (1995; Zbl 0847.46010) Full Text: DOI