Commutators and localization on the Drury-Arveson space

Quanlei Fang; Jingbo Xia

doi:10.1016/j.jfa.2010.10.013

Commutators and localization on the Drury-Arveson space

Quanlei Fang
, Jingbo Xia

Mathematics

SUNY Buffalo

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

9 Scopus citations

Abstract

Let f be a multiplier for the Drury-Arveson space H_n² of the unit ball, and let ζ₁,...,ζ_n denote the coordinate functions. We show that for each 1≤i≤n, the commutator [M_f^*,M_ζi] belongs to the Schatten class C_p, p>2n. This leads to a localization result for multipliers.

Original language	English
Pages (from-to)	639-673
Number of pages	35
Journal	Journal of Functional Analysis
Volume	260
Issue number	3
DOIs	https://doi.org/10.1016/j.jfa.2010.10.013
State	Published - Feb 15 2011

Keywords

Drury-Arveson space
Multiplier

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10.1016/j.jfa.2010.10.013

Cite this

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title = "Commutators and localization on the Drury-Arveson space",

abstract = "Let f be a multiplier for the Drury-Arveson space Hn2 of the unit ball, and let ζ1,...,ζn denote the coordinate functions. We show that for each 1≤i≤n, the commutator [Mf*,Mζi] belongs to the Schatten class Cp, p>2n. This leads to a localization result for multipliers.",

keywords = "Drury-Arveson space, Multiplier",

author = "Quanlei Fang and Jingbo Xia",

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T1 - Commutators and localization on the Drury-Arveson space

AU - Fang, Quanlei

AU - Xia, Jingbo

PY - 2011/2/15

Y1 - 2011/2/15

N2 - Let f be a multiplier for the Drury-Arveson space Hn2 of the unit ball, and let ζ1,...,ζn denote the coordinate functions. We show that for each 1≤i≤n, the commutator [Mf*,Mζi] belongs to the Schatten class Cp, p>2n. This leads to a localization result for multipliers.

AB - Let f be a multiplier for the Drury-Arveson space Hn2 of the unit ball, and let ζ1,...,ζn denote the coordinate functions. We show that for each 1≤i≤n, the commutator [Mf*,Mζi] belongs to the Schatten class Cp, p>2n. This leads to a localization result for multipliers.

KW - Drury-Arveson space

KW - Multiplier

UR - https://www.scopus.com/pages/publications/78349303902

U2 - 10.1016/j.jfa.2010.10.013

DO - 10.1016/j.jfa.2010.10.013

M3 - Article

AN - SCOPUS:78349303902

SN - 0022-1236

VL - 260

SP - 639

EP - 673

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 3

ER -

Commutators and localization on the Drury-Arveson space

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Keywords

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