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December 2008 Hilbert-Schmidt Hankel Operators and Berezin Iteration
Wolfram BAUER, Kenro FURUTANI
Tokyo J. Math. 31(2): 293-319 (December 2008). DOI: 10.3836/tjm/1233844053

Abstract

Let $H$ be a reproducing kernel Hilbert space contained in a wider space $L^2(X,\mu)$. We study the Hilbert-Schmidt property of Hankel operators $H_g$ on $H$ with bounded symbol $g$ by analyzing the behavior of the iterated Berezin transform. We determine symbol classes $\mathcal{S}$ such that for $g\in \mathcal{S}$ the Hilbert-Schmidt property of $H_g$ implies that $H_{\bar{g}}$ is a Hilbert-Schmidt operator as well and there is a norm estimate of the form $\|H_{\bar{g}}\|_{\text{HS}}\leq C\cdot \| H_g\|_{\text{HS}}$. Finally, applications to the case of Bergman spaces over strictly pseudo convex domains in $\mathbb{C}^n$, the Fock space, the pluri-harmonic Fock space and spaces of holomorphic functions on a quadric are given.

Citation

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Wolfram BAUER. Kenro FURUTANI. "Hilbert-Schmidt Hankel Operators and Berezin Iteration." Tokyo J. Math. 31 (2) 293 - 319, December 2008. https://doi.org/10.3836/tjm/1233844053

Information

Published: December 2008
First available in Project Euclid: 5 February 2009

zbMATH: 1181.47022
MathSciNet: MR2477873
Digital Object Identifier: 10.3836/tjm/1233844053

Subjects:
Primary: 47B35
Secondary: 32A25, 32Q15, 47B10, 53D50

Rights: Copyright © 2008 Publication Committee for the Tokyo Journal of Mathematics

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Vol.31 • No. 2 • December 2008
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