Reducing subspaces for multiplication operators on the Dirichlet space through local inverses and Riemann surfaces

Reducing subspaces for multiplication operators on the Dirichlet space through local inverses and Riemann surfaces

This paper gives a full characterization of the reducing subspaces for the multiplication operator Mϕ on the Dirichlet space with symbol of finite Blaschke product ϕ of order 5I 6I 7. The reducing subspaces of Mϕ on the Dirichlet space and Bergman space are related. Our strategy is to use local inve...

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Bibliographic Details
Main Authors: Gu Caixing, Luo Shuaibing, Xiao Jie
Format: Article
Language:English
Published: De Gruyter 2017-02-01
Series:Complex Manifolds
Subjects:
reducing subspace
multiplication operator
dirichlet space
blaschke product
local inverse
riemann surface
47b35
46e22
Online Access:https://doi.org/10.1515/coma-2017-0007
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spelling doaj-e267cf83995b49aabb2ca8028a78e8312021-09-06T19:19:41ZengDe GruyterComplex Manifolds2300-74432017-02-01418411910.1515/coma-2017-0007coma-2017-0007Reducing subspaces for multiplication operators on the Dirichlet space through local inverses and Riemann surfacesGu Caixing0Luo Shuaibing1Xiao Jie2Department of Mathematics, California Polytechnic State University, San Luis Obispo, CA 93407, United States of AmericaCollege of Mathematics and Econometrics, Hunan University, Changsha, Hunan, 410082, ChinaDepartment of Mathematics and Statistics, Memorial University, St. John’s, NL A1C5S7, CanadaThis paper gives a full characterization of the reducing subspaces for the multiplication operator Mϕ on the Dirichlet space with symbol of finite Blaschke product ϕ of order 5I 6I 7. The reducing subspaces of Mϕ on the Dirichlet space and Bergman space are related. Our strategy is to use local inverses and Riemann surfaces to study the reducing subspaces of Mϕ on the Bergman space. By this means, we determine the reducing subspaces of Mϕ on the Dirichlet space and answer some questions of Douglas-Putinar-Wang in [6].https://doi.org/10.1515/coma-2017-0007reducing subspacemultiplication operatordirichlet spaceblaschke productlocal inverseriemann surface47b3546e22
collection DOAJ
language English
format Article
sources DOAJ
author Gu Caixing
Luo Shuaibing
Xiao Jie
spellingShingle Gu Caixing
Luo Shuaibing
Xiao Jie
Reducing subspaces for multiplication operators on the Dirichlet space through local inverses and Riemann surfaces
Complex Manifolds
reducing subspace
multiplication operator
dirichlet space
blaschke product
local inverse
riemann surface
47b35
46e22
author_facet Gu Caixing
Luo Shuaibing
Xiao Jie
author_sort Gu Caixing
title Reducing subspaces for multiplication operators on the Dirichlet space through local inverses and Riemann surfaces
title_short Reducing subspaces for multiplication operators on the Dirichlet space through local inverses and Riemann surfaces
title_full Reducing subspaces for multiplication operators on the Dirichlet space through local inverses and Riemann surfaces
title_fullStr Reducing subspaces for multiplication operators on the Dirichlet space through local inverses and Riemann surfaces
title_full_unstemmed Reducing subspaces for multiplication operators on the Dirichlet space through local inverses and Riemann surfaces
title_sort reducing subspaces for multiplication operators on the dirichlet space through local inverses and riemann surfaces
publisher De Gruyter
series Complex Manifolds
issn 2300-7443
publishDate 2017-02-01
description This paper gives a full characterization of the reducing subspaces for the multiplication operator Mϕ on the Dirichlet space with symbol of finite Blaschke product ϕ of order 5I 6I 7. The reducing subspaces of Mϕ on the Dirichlet space and Bergman space are related. Our strategy is to use local inverses and Riemann surfaces to study the reducing subspaces of Mϕ on the Bergman space. By this means, we determine the reducing subspaces of Mϕ on the Dirichlet space and answer some questions of Douglas-Putinar-Wang in [6].
topic reducing subspace
multiplication operator
dirichlet space
blaschke product
local inverse
riemann surface
47b35
46e22
url https://doi.org/10.1515/coma-2017-0007
work_keys_str_mv AT gucaixing reducingsubspacesformultiplicationoperatorsonthedirichletspacethroughlocalinversesandriemannsurfaces
AT luoshuaibing reducingsubspacesformultiplicationoperatorsonthedirichletspacethroughlocalinversesandriemannsurfaces
AT xiaojie reducingsubspacesformultiplicationoperatorsonthedirichletspacethroughlocalinversesandriemannsurfaces
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