The Essential Norm of Operators on Apα(Bn)

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...

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Autores principales: Mitkovski, M., Suárez, D., Wick, B.D.
Formato: JOUR
Materias:
Berezin transform
Bergman space
compact operators
essential norm
Toeplitz algebra
Toeplitz operator
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_0378620X_v75_n2_p197_Mitkovski
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_0378620X_v75_n2_p197_Mitkovski
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spelling todo:paper_0378620X_v75_n2_p197_Mitkovski2023-10-03T15:33:13Z The Essential Norm of Operators on Apα(Bn) Mitkovski, M. Suárez, D. Wick, B.D. Berezin transform Bergman space compact operators essential norm Toeplitz algebra Toeplitz operator 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. © 2012 Springer Basel. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_0378620X_v75_n2_p197_Mitkovski
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Berezin transform
Bergman space
compact operators
essential norm
Toeplitz algebra
Toeplitz operator
spellingShingle Berezin transform
Bergman space
compact operators
essential norm
Toeplitz algebra
Toeplitz operator
Mitkovski, M.
Suárez, D.
Wick, B.D.
The Essential Norm of Operators on Apα(Bn)
topic_facet Berezin transform
Bergman space
compact operators
essential norm
Toeplitz algebra
Toeplitz operator
description 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. © 2012 Springer Basel.
format JOUR
author Mitkovski, M.
Suárez, D.
Wick, B.D.
author_facet Mitkovski, M.
Suárez, D.
Wick, B.D.
author_sort Mitkovski, M.
title The Essential Norm of Operators on Apα(Bn)
title_short The Essential Norm of Operators on Apα(Bn)
title_full The Essential Norm of Operators on Apα(Bn)
title_fullStr The Essential Norm of Operators on Apα(Bn)
title_full_unstemmed The Essential Norm of Operators on Apα(Bn)
title_sort essential norm of operators on apα(bn)
url http://hdl.handle.net/20.500.12110/paper_0378620X_v75_n2_p197_Mitkovski
work_keys_str_mv AT mitkovskim theessentialnormofoperatorsonapabn
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AT wickbd theessentialnormofoperatorsonapabn
AT mitkovskim essentialnormofoperatorsonapabn
AT suarezd essentialnormofoperatorsonapabn
AT wickbd essentialnormofoperatorsonapabn
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