On the essential commutant of the Toeplitz algebra on the Bergman space

Jingbo Xia

doi:10.1016/j.jfa.2017.01.020

On the essential commutant of the Toeplitz algebra on the Bergman space

Jingbo Xia

Mathematics

University at Buffalo

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

4 Scopus citations

Abstract

Let T be the C^⁎-algebra generated by the Toeplitz operators {T_f:f∈L^∞(B,dv)} on the Bergman space of the unit ball. We show that the essential commutant of T equals {T_g:g∈VO_bdd}+K, where VO_bdd is the collection of bounded functions of vanishing oscillation on B and K denotes the collection of compact operators on L_a²(B,dv).

Original language	English
Pages (from-to)	5191-5217
Number of pages	27
Journal	Journal of Functional Analysis
Volume	272
Issue number	12
DOIs	https://doi.org/10.1016/j.jfa.2017.01.020
State	Published - Jun 15 2017

Keywords

Bergman space
Essential commutant
Toeplitz algebra

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10.1016/j.jfa.2017.01.020

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title = "On the essential commutant of the Toeplitz algebra on the Bergman space",

abstract = "Let T be the C⁎-algebra generated by the Toeplitz operators \{Tf:f∈L∞(B,dv)\} on the Bergman space of the unit ball. We show that the essential commutant of T equals \{Tg:g∈VObdd\}+K, where VObdd is the collection of bounded functions of vanishing oscillation on B and K denotes the collection of compact operators on La2(B,dv).",

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AU - Xia, Jingbo

PY - 2017/6/15

Y1 - 2017/6/15

N2 - Let T be the C⁎-algebra generated by the Toeplitz operators {Tf:f∈L∞(B,dv)} on the Bergman space of the unit ball. We show that the essential commutant of T equals {Tg:g∈VObdd}+K, where VObdd is the collection of bounded functions of vanishing oscillation on B and K denotes the collection of compact operators on La2(B,dv).

AB - Let T be the C⁎-algebra generated by the Toeplitz operators {Tf:f∈L∞(B,dv)} on the Bergman space of the unit ball. We show that the essential commutant of T equals {Tg:g∈VObdd}+K, where VObdd is the collection of bounded functions of vanishing oscillation on B and K denotes the collection of compact operators on La2(B,dv).

KW - Bergman space

KW - Essential commutant

KW - Toeplitz algebra

UR - https://www.scopus.com/pages/publications/85011818909

U2 - 10.1016/j.jfa.2017.01.020

DO - 10.1016/j.jfa.2017.01.020

M3 - Article

SN - 0022-1236

VL - 272

SP - 5191

EP - 5217

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 12

ER -

On the essential commutant of the Toeplitz algebra on the Bergman space

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Keywords

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