Commutative C⁎-Algebras of Toeplitz Operators via the Moment Map on the Polydisk

Commutative C⁎-Algebras of Toeplitz Operators via the Moment Map on the Polydisk

We found that in the polydisk Dn there exist (n+1)(n+2)/2 different classes of commutative C⁎-algebras generated by Toeplitz operators whose symbols are invariant under the action of maximal Abelian subgroups of biholomorphisms. On the other hand, using the moment map associated with each (not neces...

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Main Authors: Mauricio Hernández-Marroquin, Armando Sánchez-Nungaray, Luis Alfredo Dupont-García
Format: Article
Language:English
Published: Hindawi Limited 2016-01-01
Series:Journal of Function Spaces
Online Access:http://dx.doi.org/10.1155/2016/1652719
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spelling doaj-f514c39f4f0340b19b78f95e5ae8b1ad2020-11-25T00:37:15ZengHindawi LimitedJournal of Function Spaces2314-88962314-88882016-01-01201610.1155/2016/16527191652719Commutative C⁎-Algebras of Toeplitz Operators via the Moment Map on the PolydiskMauricio Hernández-Marroquin0Armando Sánchez-Nungaray1Luis Alfredo Dupont-García2Facultad de Matemáticas, Universidad Veracruzana, Lomas del Estadio S/N, 91000 Xalapa, VER, MexicoFacultad de Matemáticas, Universidad Veracruzana, Lomas del Estadio S/N, 91000 Xalapa, VER, MexicoFacultad de Matemáticas, Universidad Veracruzana, Lomas del Estadio S/N, 91000 Xalapa, VER, MexicoWe found that in the polydisk Dn there exist (n+1)(n+2)/2 different classes of commutative C⁎-algebras generated by Toeplitz operators whose symbols are invariant under the action of maximal Abelian subgroups of biholomorphisms. On the other hand, using the moment map associated with each (not necessary maximal) Abelian subgroup of biholomorphism we introduced a family of symbols given by the moment map such that the C⁎-algebra generated by Toeplitz operators with this kind of symbol is commutative. Thus we relate to each Abelian subgroup of biholomorphisms a commutative C⁎-algebra of Toeplitz operators.http://dx.doi.org/10.1155/2016/1652719
collection DOAJ
language English
format Article
sources DOAJ
author Mauricio Hernández-Marroquin
Armando Sánchez-Nungaray
Luis Alfredo Dupont-García
spellingShingle Mauricio Hernández-Marroquin
Armando Sánchez-Nungaray
Luis Alfredo Dupont-García
Commutative C⁎-Algebras of Toeplitz Operators via the Moment Map on the Polydisk
Journal of Function Spaces
author_facet Mauricio Hernández-Marroquin
Armando Sánchez-Nungaray
Luis Alfredo Dupont-García
author_sort Mauricio Hernández-Marroquin
title Commutative C⁎-Algebras of Toeplitz Operators via the Moment Map on the Polydisk
title_short Commutative C⁎-Algebras of Toeplitz Operators via the Moment Map on the Polydisk
title_full Commutative C⁎-Algebras of Toeplitz Operators via the Moment Map on the Polydisk
title_fullStr Commutative C⁎-Algebras of Toeplitz Operators via the Moment Map on the Polydisk
title_full_unstemmed Commutative C⁎-Algebras of Toeplitz Operators via the Moment Map on the Polydisk
title_sort commutative c⁎-algebras of toeplitz operators via the moment map on the polydisk
publisher Hindawi Limited
series Journal of Function Spaces
issn 2314-8896
2314-8888
publishDate 2016-01-01
description We found that in the polydisk Dn there exist (n+1)(n+2)/2 different classes of commutative C⁎-algebras generated by Toeplitz operators whose symbols are invariant under the action of maximal Abelian subgroups of biholomorphisms. On the other hand, using the moment map associated with each (not necessary maximal) Abelian subgroup of biholomorphism we introduced a family of symbols given by the moment map such that the C⁎-algebra generated by Toeplitz operators with this kind of symbol is commutative. Thus we relate to each Abelian subgroup of biholomorphisms a commutative C⁎-algebra of Toeplitz operators.
url http://dx.doi.org/10.1155/2016/1652719
work_keys_str_mv AT mauriciohernandezmarroquin commutativecalgebrasoftoeplitzoperatorsviathemomentmaponthepolydisk
AT armandosancheznungaray commutativecalgebrasoftoeplitzoperatorsviathemomentmaponthepolydisk
AT luisalfredodupontgarcia commutativecalgebrasoftoeplitzoperatorsviathemomentmaponthepolydisk
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