The Essential Norm of Operators on Apα(Bn)

Mishko Mitkovski; Daniel Suárez; Brett D. Wick

doi:10.1007/s00020-012-2025-1

The Essential Norm of Operators on A^p_α(B_n)

Mishko Mitkovski
, Daniel Suárez
, Brett D. Wick

Department of Mathematics

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

44 Scopus citations

Abstract

In this paper we characterize the compact operators on the weighted Bergman spaces A^pα(B_n) when 1 < p < ∞ and α > -1. The main result shows that an operator on A^p_α(B_n) is compact if and only if it belongs to the Toeplitz algebra and its Berezin transform vanishes on the boundary of the ball.

Original language	English
Pages (from-to)	197-233
Number of pages	37
Journal	Integral Equations and Operator Theory
Volume	75
Issue number	2
DOIs	https://doi.org/10.1007/s00020-012-2025-1
State	Published - Feb 2013

Keywords

Berezin transform
Bergman space
compact operators
essential norm
Toeplitz algebra
Toeplitz operator

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10.1007/s00020-012-2025-1

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abstract = "In this paper we characterize the compact operators on the weighted Bergman spaces Apα(Bn) when 1 < p < ∞ and α > -1. The main result shows that an operator on Apα(Bn) is compact if and only if it belongs to the Toeplitz algebra and its Berezin transform vanishes on the boundary of the ball.",

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AU - Suárez, Daniel

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N2 - In this paper we characterize the compact operators on the weighted Bergman spaces Apα(Bn) when 1 < p < ∞ and α > -1. The main result shows that an operator on Apα(Bn) is compact if and only if it belongs to the Toeplitz algebra and its Berezin transform vanishes on the boundary of the ball.

AB - In this paper we characterize the compact operators on the weighted Bergman spaces Apα(Bn) when 1 < p < ∞ and α > -1. The main result shows that an operator on Apα(Bn) is compact if and only if it belongs to the Toeplitz algebra and its Berezin transform vanishes on the boundary of the ball.

KW - Berezin transform

KW - Bergman space

KW - compact operators

KW - essential norm

KW - Toeplitz algebra

KW - Toeplitz operator

UR - https://www.scopus.com/pages/publications/84872612319

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DO - 10.1007/s00020-012-2025-1

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EP - 233

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

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ER -

The Essential Norm of Operators on A^p_α(B_n)

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Keywords

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