A double commutant relation in the Calkin algebra on the Bergman space

Jingbo Xia

doi:10.1016/j.jfa.2017.11.004

A double commutant relation in the Calkin algebra on the Bergman space

Jingbo Xia

Mathematics

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

8 Scopus citations

Abstract

Let T be the Toeplitz algebra on the Bergman space L_a ²(B,dv) of the unit ball in Cⁿ. We show that the image of T in the Calkin algebra satisfies the double commutant relation: π(T)={π(T)}^″. This is a surprising result, for it is the opposite of what happens in the Hardy-space case [16,17].

Original language	English
Pages (from-to)	1631-1656
Number of pages	26
Journal	Journal of Functional Analysis
Volume	274
Issue number	6
DOIs	https://doi.org/10.1016/j.jfa.2017.11.004
State	Published - Mar 15 2018

Keywords

Bergman space
Calkin algebra
Double commutant relation
Toeplitz algebra

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10.1016/j.jfa.2017.11.004

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title = "A double commutant relation in the Calkin algebra on the Bergman space",

abstract = "Let T be the Toeplitz algebra on the Bergman space La 2(B,dv) of the unit ball in Cn. We show that the image of T in the Calkin algebra satisfies the double commutant relation: π(T)=\{π(T)\}″. This is a surprising result, for it is the opposite of what happens in the Hardy-space case [16,17].",

keywords = "Bergman space, Calkin algebra, Double commutant relation, Toeplitz algebra",

author = "Jingbo Xia",

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AU - Xia, Jingbo

PY - 2018/3/15

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N2 - Let T be the Toeplitz algebra on the Bergman space La 2(B,dv) of the unit ball in Cn. We show that the image of T in the Calkin algebra satisfies the double commutant relation: π(T)={π(T)}″. This is a surprising result, for it is the opposite of what happens in the Hardy-space case [16,17].

AB - Let T be the Toeplitz algebra on the Bergman space La 2(B,dv) of the unit ball in Cn. We show that the image of T in the Calkin algebra satisfies the double commutant relation: π(T)={π(T)}″. This is a surprising result, for it is the opposite of what happens in the Hardy-space case [16,17].

KW - Bergman space

KW - Calkin algebra

KW - Double commutant relation

KW - Toeplitz algebra

UR - https://www.scopus.com/pages/publications/85034414884

U2 - 10.1016/j.jfa.2017.11.004

DO - 10.1016/j.jfa.2017.11.004

M3 - Article

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SN - 0022-1236

VL - 274

SP - 1631

EP - 1656

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 6

ER -

A double commutant relation in the Calkin algebra on the Bergman space

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Keywords

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