Schatten class Hankel operators on doubling Fock spaces and the Berger-Coburn phenomenon

Fuente: arXiv
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Autori principali: Asghari, Ghazaleh, Virtanen, Jani A., Hu, Zhangjian
Natura: Preprint
Pubblicazione: 2023
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author Asghari, Ghazaleh
Virtanen, Jani A.
Hu, Zhangjian
author_facet Asghari, Ghazaleh
Virtanen, Jani A.
Hu, Zhangjian
contents Using the notion of integral distance to analytic functions, we give a characterization of Schatten class Hankel operators acting on doubling Fock spaces on the complex plane and use it to show that for $f\in L^{\infty}$, if $H_{f}$ is Hilbert-Schmidt, then so is $H_{\bar{f}}$. This property is known as the Berger-Coburn phenomenon. When $0<p\le 1$, we show that the Berger-Coburn phenomenon fails for a large class of doubling Fock spaces. Along the way, we illustrate our results for the canonical weights $|z|^m$ when $m>0$.
format Preprint
id arxiv_https___arxiv_org_abs_2312_06656
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Schatten class Hankel operators on doubling Fock spaces and the Berger-Coburn phenomenon
Asghari, Ghazaleh
Virtanen, Jani A.
Hu, Zhangjian
Functional Analysis
Using the notion of integral distance to analytic functions, we give a characterization of Schatten class Hankel operators acting on doubling Fock spaces on the complex plane and use it to show that for $f\in L^{\infty}$, if $H_{f}$ is Hilbert-Schmidt, then so is $H_{\bar{f}}$. This property is known as the Berger-Coburn phenomenon. When $0<p\le 1$, we show that the Berger-Coburn phenomenon fails for a large class of doubling Fock spaces. Along the way, we illustrate our results for the canonical weights $|z|^m$ when $m>0$.
title Schatten class Hankel operators on doubling Fock spaces and the Berger-Coburn phenomenon
topic Functional Analysis
url https://arxiv.org/abs/2312.06656