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

• Autorzy: Caixing Gu , Shuaibing Luo , Jie Xiao
• Języki publikacji: EN

Abstrakty

EN

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].

Słowa kluczowe

EN

Reducing subspace; Multiplication operator; Dirichlet space; Blaschke product; Local inverse; Riemann surface

Kategorie tematyczne

• 46E22: Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces)
• 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators

• Wydawca: De Gruyter Open
• Czasopismo: Complex Manifolds
• Rocznik: 2017
• Tom: 4
• Numer: 1
• Strony: 84-119

Daty

wydano

2017-02-23

otrzymano

2017-01-25

zaakceptowano

2017-06-12

online

2017-07-05

Twórcy

autor

Caixing Gu

• , CA 93407,

autor

Shuaibing Luo

• , 410082,

autor

Jie Xiao

• , NL A1C5S7,

Identyfikatory

DOI

10.1515/coma-2017-0007