A generalization of Toeplitz operators on the Bergman space

If μ is a finite measure on the unit disc and k ≥ 0 is an integer, we study a generalization derived from Engliš's work, T<inf>μ</inf>(k) m, of the traditional Toeplitz operators on the Bergman space A2, which are the case k = 0. Among other things, we prove that when μ ≥ 0, these o...

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Autor principal: Suárez, D.
Formato: JOUR
Materias:
Berezin transform
Bergman space
Toeplitz operators
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_03794024_v73_n2_p315_Suarez
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_03794024_v73_n2_p315_Suarez
record_format dspace
spelling todo:paper_03794024_v73_n2_p315_Suarez2023-10-03T15:33:26Z A generalization of Toeplitz operators on the Bergman space Suárez, D. Berezin transform Bergman space Toeplitz operators If μ is a finite measure on the unit disc and k ≥ 0 is an integer, we study a generalization derived from Engliš's work, T<inf>μ</inf>(k) m, of the traditional Toeplitz operators on the Bergman space A2, which are the case k = 0. Among other things, we prove that when μ ≥ 0, these operators are bounded if and only if μ is a Carleson measure, they are compact if and only if μ is a vanishing Carleson measure, and we obtain some estimates for their norms. Also, we use these operators to characterize the closure of the image of the Berezin transform applied to the whole operator algebra. © by THETA, 2015. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_03794024_v73_n2_p315_Suarez
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
Toeplitz operators
spellingShingle Berezin transform
Bergman space
Toeplitz operators
Suárez, D.
A generalization of Toeplitz operators on the Bergman space
topic_facet Berezin transform
Bergman space
Toeplitz operators
description If μ is a finite measure on the unit disc and k ≥ 0 is an integer, we study a generalization derived from Engliš's work, T<inf>μ</inf>(k) m, of the traditional Toeplitz operators on the Bergman space A2, which are the case k = 0. Among other things, we prove that when μ ≥ 0, these operators are bounded if and only if μ is a Carleson measure, they are compact if and only if μ is a vanishing Carleson measure, and we obtain some estimates for their norms. Also, we use these operators to characterize the closure of the image of the Berezin transform applied to the whole operator algebra. © by THETA, 2015.
format JOUR
author Suárez, D.
author_facet Suárez, D.
author_sort Suárez, D.
title A generalization of Toeplitz operators on the Bergman space
title_short A generalization of Toeplitz operators on the Bergman space
title_full A generalization of Toeplitz operators on the Bergman space
title_fullStr A generalization of Toeplitz operators on the Bergman space
title_full_unstemmed A generalization of Toeplitz operators on the Bergman space
title_sort generalization of toeplitz operators on the bergman space
url http://hdl.handle.net/20.500.12110/paper_03794024_v73_n2_p315_Suarez
work_keys_str_mv AT suarezd ageneralizationoftoeplitzoperatorsonthebergmanspace
AT suarezd generalizationoftoeplitzoperatorsonthebergmanspace
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