Products of Hankel operators on the Fock space

Pan Ma; Fugang Yan; Dechao Zheng; Kehe Zhu

doi:10.1016/j.jfa.2019.01.003

Products of Hankel operators on the Fock space

Pan Ma
, Fugang Yan
, Dechao Zheng
, Kehe Zhu

Mathematics and Statistics

University at Albany

Central South University
Chongqing University
State University of New York (SUNY)
Vanderbilt University

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

For entire functions f and g we study the problem of when the Hankel product H_f‾ ^⁎H_g‾ is bounded or compact on the Fock space F_α ². This is a companion to Sarason's Toeplitz product problem which was completely solved for the Fock space by Cho–Park–Zhu in 2014. Surprisingly, our results here are different from the natural conjectures motivated by the Toeplitz product problem.

Original language	English
Pages (from-to)	2644-2663
Number of pages	20
Journal	Journal of Functional Analysis
Volume	277
Issue number	8
DOIs	https://doi.org/10.1016/j.jfa.2019.01.003
State	Published - Oct 15 2019

Keywords

Berezin transform
Fock space
Hankel operators
Toeplitz operators

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10.1016/j.jfa.2019.01.003

Cite this

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title = "Products of Hankel operators on the Fock space",

abstract = "For entire functions f and g we study the problem of when the Hankel product Hf‾ ⁎Hg‾ is bounded or compact on the Fock space Fα 2. This is a companion to Sarason's Toeplitz product problem which was completely solved for the Fock space by Cho–Park–Zhu in 2014. Surprisingly, our results here are different from the natural conjectures motivated by the Toeplitz product problem.",

keywords = "Berezin transform, Fock space, Hankel operators, Toeplitz operators",

author = "Pan Ma and Fugang Yan and Dechao Zheng and Kehe Zhu",

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T1 - Products of Hankel operators on the Fock space

AU - Ma, Pan

AU - Yan, Fugang

AU - Zheng, Dechao

AU - Zhu, Kehe

PY - 2019/10/15

Y1 - 2019/10/15

N2 - For entire functions f and g we study the problem of when the Hankel product Hf‾ ⁎Hg‾ is bounded or compact on the Fock space Fα 2. This is a companion to Sarason's Toeplitz product problem which was completely solved for the Fock space by Cho–Park–Zhu in 2014. Surprisingly, our results here are different from the natural conjectures motivated by the Toeplitz product problem.

AB - For entire functions f and g we study the problem of when the Hankel product Hf‾ ⁎Hg‾ is bounded or compact on the Fock space Fα 2. This is a companion to Sarason's Toeplitz product problem which was completely solved for the Fock space by Cho–Park–Zhu in 2014. Surprisingly, our results here are different from the natural conjectures motivated by the Toeplitz product problem.

KW - Berezin transform

KW - Fock space

KW - Hankel operators

KW - Toeplitz operators

UR - https://www.scopus.com/pages/publications/85060104744

U2 - 10.1016/j.jfa.2019.01.003

DO - 10.1016/j.jfa.2019.01.003

M3 - Article

SN - 0022-1236

VL - 277

SP - 2644

EP - 2663

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 8

ER -

Products of Hankel operators on the Fock space

Abstract

Keywords

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