Membership of hankel operators on the ball in unitary ideals

Jonathan Arazy

doi:10.1112/jlms/s2-43.3.485

Membership of hankel operators on the ball in unitary ideals

Jonathan Arazy

Department of Mathematics

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

Abstract

We consider Hankel operators on (weighted) Bergman spaces on the unit ball in several complex variables. The main result is several, equivalent, necessary and sufficient conditions for a Hankel operator with analytic symbol to belong to the Schatten-von Neumann ideal S_p. There is one important difference between our results, and the corresponding results in one variable; if the number of dimensions N is 2 or more, there exist non-trivial Hankel operators with analytic symbols in S_pwhen p > 2N, but if N = 1, the condition is p > 1. One ingredient in the proof is an improvement of Russo’s condition for integral operators on L⁸to belong to S_p.

Original language	English
Pages (from-to)	485-508
Number of pages	24
Journal	Journal of the London Mathematical Society
Volume	s2-43
Issue number	3
DOIs	https://doi.org/10.1112/jlms/s2-43.3.485
State	Published - Jun 1991

Bibliographical note

Funding Information:
Acknowledgement. The results of this paper are the outcome of discussions among the authors at a workshop at Munkfors, Sweden, sponsored by the ' Civilingenjor Gustaf Sigurd Magnusons fond for framjande av vetenskapen inom amnet matematik' of the Royal Swedish Academy of Sciences (Kungl. Vetenskapsakademien).

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1112/jlms/s2-43.3.485

Cite this

@article{01f47e9ef2e54f00a1be37166a36e1f6,

title = "Membership of hankel operators on the ball in unitary ideals",

abstract = "We consider Hankel operators on (weighted) Bergman spaces on the unit ball in several complex variables. The main result is several, equivalent, necessary and sufficient conditions for a Hankel operator with analytic symbol to belong to the Schatten-von Neumann ideal Sp. There is one important difference between our results, and the corresponding results in one variable; if the number of dimensions N is 2 or more, there exist non-trivial Hankel operators with analytic symbols in Spwhen p > 2N, but if N = 1, the condition is p > 1. One ingredient in the proof is an improvement of Russo{\textquoteright}s condition for integral operators on L8to belong to Sp.",

author = "Jonathan Arazy",

note = "Funding Information: Acknowledgement. The results of this paper are the outcome of discussions among the authors at a workshop at Munkfors, Sweden, sponsored by the ' Civilingenjor Gustaf Sigurd Magnusons fond for framjande av vetenskapen inom amnet matematik' of the Royal Swedish Academy of Sciences (Kungl. Vetenskapsakademien).",

year = "1991",

month = jun,

doi = "10.1112/jlms/s2-43.3.485",

language = "English",

volume = "s2-43",

pages = "485--508",

journal = "Journal of the London Mathematical Society",

issn = "0024-6107",

publisher = "John Wiley and Sons Ltd",

number = "3",

}

TY - JOUR

T1 - Membership of hankel operators on the ball in unitary ideals

AU - Arazy, Jonathan

N1 - Funding Information: Acknowledgement. The results of this paper are the outcome of discussions among the authors at a workshop at Munkfors, Sweden, sponsored by the ' Civilingenjor Gustaf Sigurd Magnusons fond for framjande av vetenskapen inom amnet matematik' of the Royal Swedish Academy of Sciences (Kungl. Vetenskapsakademien).

PY - 1991/6

Y1 - 1991/6

N2 - We consider Hankel operators on (weighted) Bergman spaces on the unit ball in several complex variables. The main result is several, equivalent, necessary and sufficient conditions for a Hankel operator with analytic symbol to belong to the Schatten-von Neumann ideal Sp. There is one important difference between our results, and the corresponding results in one variable; if the number of dimensions N is 2 or more, there exist non-trivial Hankel operators with analytic symbols in Spwhen p > 2N, but if N = 1, the condition is p > 1. One ingredient in the proof is an improvement of Russo’s condition for integral operators on L8to belong to Sp.

AB - We consider Hankel operators on (weighted) Bergman spaces on the unit ball in several complex variables. The main result is several, equivalent, necessary and sufficient conditions for a Hankel operator with analytic symbol to belong to the Schatten-von Neumann ideal Sp. There is one important difference between our results, and the corresponding results in one variable; if the number of dimensions N is 2 or more, there exist non-trivial Hankel operators with analytic symbols in Spwhen p > 2N, but if N = 1, the condition is p > 1. One ingredient in the proof is an improvement of Russo’s condition for integral operators on L8to belong to Sp.

UR - http://www.scopus.com/inward/record.url?scp=0001036061&partnerID=8YFLogxK

U2 - 10.1112/jlms/s2-43.3.485

DO - 10.1112/jlms/s2-43.3.485

M3 - Article

AN - SCOPUS:0001036061

SN - 0024-6107

VL - s2-43

SP - 485

EP - 508

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

IS - 3

ER -

Membership of hankel operators on the ball in unitary ideals

Abstract

Bibliographical note

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this