The Berger–Coburn Phenomenon for Hankel Operators on the Fock Space

Jingbo Xia

doi:10.1007/s11785-023-01338-8

The Berger–Coburn Phenomenon for Hankel Operators on the Fock Space

Jingbo Xia

Mathematics

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

4 Scopus citations

Abstract

The Berger–Coburn phenomenon of Hankel operators was recently reported by Hu and Virtanen for the Schatten classes C_p, 1 < p< ∞. But a careful reading of [14] finds that in the case 1 < p< 2 , there is a technical problem in their proof. In this paper we first fix this problem. We then establish the Berger–Coburn phenomenon for the Lorentz ideals Cp+ and Cp-, 1 < p< ∞. Last but not least, we show that there is no Berger–Coburn phenomenon for the trace class C₁, for C1+, and for the Macaev ideal C∞-.

Original language	English
Article number	35
Journal	Complex Analysis and Operator Theory
Volume	17
Issue number	3
DOIs	https://doi.org/10.1007/s11785-023-01338-8
State	Published - Apr 2023

Keywords

Fock space
Hankel operator
Trace class

Access to Document

10.1007/s11785-023-01338-8

Cite this

@article{f293328d0c1e429b98aaaa192aa6bfb4,

title = "The Berger–Coburn Phenomenon for Hankel Operators on the Fock Space",

abstract = "The Berger–Coburn phenomenon of Hankel operators was recently reported by Hu and Virtanen for the Schatten classes Cp, 1 < p< ∞. But a careful reading of [14] finds that in the case 1 < p< 2 , there is a technical problem in their proof. In this paper we first fix this problem. We then establish the Berger–Coburn phenomenon for the Lorentz ideals Cp+ and Cp-, 1 < p< ∞. Last but not least, we show that there is no Berger–Coburn phenomenon for the trace class C1, for C1+, and for the Macaev ideal C∞-.",

keywords = "Fock space, Hankel operator, Trace class",

author = "Jingbo Xia",

note = "Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.",

year = "2023",

month = apr,

doi = "10.1007/s11785-023-01338-8",

language = "English",

volume = "17",

journal = "Complex Analysis and Operator Theory",

issn = "1661-8254",

publisher = "Springer International Publishing",

number = "3",

}

TY - JOUR

T1 - The Berger–Coburn Phenomenon for Hankel Operators on the Fock Space

AU - Xia, Jingbo

PY - 2023/4

Y1 - 2023/4

N2 - The Berger–Coburn phenomenon of Hankel operators was recently reported by Hu and Virtanen for the Schatten classes Cp, 1 < p< ∞. But a careful reading of [14] finds that in the case 1 < p< 2 , there is a technical problem in their proof. In this paper we first fix this problem. We then establish the Berger–Coburn phenomenon for the Lorentz ideals Cp+ and Cp-, 1 < p< ∞. Last but not least, we show that there is no Berger–Coburn phenomenon for the trace class C1, for C1+, and for the Macaev ideal C∞-.

AB - The Berger–Coburn phenomenon of Hankel operators was recently reported by Hu and Virtanen for the Schatten classes Cp, 1 < p< ∞. But a careful reading of [14] finds that in the case 1 < p< 2 , there is a technical problem in their proof. In this paper we first fix this problem. We then establish the Berger–Coburn phenomenon for the Lorentz ideals Cp+ and Cp-, 1 < p< ∞. Last but not least, we show that there is no Berger–Coburn phenomenon for the trace class C1, for C1+, and for the Macaev ideal C∞-.

KW - Fock space

KW - Hankel operator

KW - Trace class

UR - https://www.scopus.com/pages/publications/85148994744

U2 - 10.1007/s11785-023-01338-8

DO - 10.1007/s11785-023-01338-8

M3 - Article

AN - SCOPUS:85148994744

SN - 1661-8254

VL - 17

JO - Complex Analysis and Operator Theory

JF - Complex Analysis and Operator Theory

IS - 3

M1 - 35

ER -

The Berger–Coburn Phenomenon for Hankel Operators on the Fock Space

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this