scholarly journals On Similarity and Reducing Subspaces of the n-Shift plus Certain Weighted Volterra Operator

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Yucheng Li ◽  
Hao Chen ◽  
Wenhua Lan
Keyword(s):  
Hilbert Space ◽  
Bergman Space ◽  
Volterra Operator ◽  
Multiplication Operator ◽  
Degree Polynomial ◽  
Reducing Subspaces

Let g(z) be an n-degree polynomial (n≥2). Inspired by Sarason’s result, we introduce the operator T1 defined by the multiplication operator Mg plus the weighted Volterra operator Vg on the Bergman space. We show that the operator T1 is similar to Mg on some Hilbert space Sg2(D). Then for g(z)=zn, by using matrix manipulations, the reducing subspaces of the corresponding operator T2 on the Bergman space are characterized.

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

2017 ◽  
Vol 4 (1) ◽  
pp. 84-119 ◽  
Author(s):  
Caixing Gu ◽  
Shuaibing Luo ◽  
Jie Xiao
Keyword(s):  
Bergman Space ◽  
Blaschke Product ◽  
Riemann Surfaces ◽  
Dirichlet Space ◽  
Multiplication Operator ◽  
Multiplication Operators ◽  
Finite Blaschke Product ◽  
Full Characterization ◽  
Reducing Subspaces

AbstractThis 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].

scholarly journals Classification of Reducing Subspaces of a Class of Multiplication Operators on the Bergman Space via the Hardy Space of the Bidisk

2010 ◽  
Vol 62 (2) ◽  
pp. 415-438 ◽  
Author(s):  
Shunhua Sun ◽  
Dechao Zheng ◽  
Changyong Zhong
Keyword(s):  
Hardy Space ◽  
Unit Disk ◽  
Bergman Space ◽  
Blaschke Product ◽  
Multiplication Operator ◽  
Multiplication Operators ◽  
Reducing Subspaces

AbstractIn this paper we obtain a complete description of nontrivial minimal reducing subspaces of the multiplication operator by a Blaschke product with four zeros on the Bergman space of the unit disk via the Hardy space of the bidisk.

scholarly journals Reducing subspaces for analytic multipliers of the Bergman space

2012 ◽  
Vol 263 (6) ◽  
pp. 1744-1765 ◽  
Author(s):  
Ronald G. Douglas ◽  
Mihai Putinar ◽  
Kai Wang
Keyword(s):  
Bergman Space ◽  
Reducing Subspaces

scholarly journals Reducing Subspaces of Some Multiplication Operators on the Bergman Space over Polydisk

2015 ◽  
Vol 2015 ◽  
pp. 1-12
Author(s):  
Yanyue Shi ◽  
Na Zhou
Keyword(s):  
Bergman Space ◽  
Multiplication Operators ◽  
Direct Sum ◽  
Reducing Subspace ◽  
Reducing Subspaces

We consider the reducing subspaces ofMzNonAα2(Dk), wherek≥3,zN=z1N1⋯zkNk, andNi≠Njfori≠j. We prove that each reducing subspace ofMzNis a direct sum of some minimal reducing subspaces. We also characterize the minimal reducing subspaces in the cases thatα=0andα∈(-1,+∞)∖Q, respectively. Finally, we give a complete description of minimal reducing subspaces ofMzNonAα2(D3)withα>-1.

Some Norm one Functions of the Volterra Operator

2015 ◽  
Vol 65 (6) ◽  
Author(s):  
L. Khadkhuu ◽  
D. Tsedenbayar
Keyword(s):  
Hilbert Space ◽  
Volterra Operator ◽  
Accretive Operator ◽  
Complex Hilbert Space

AbstractLet B be an accretive operator on a complex Hilbert space and let V be the classical Volterra operator on L

scholarly journals On Some Properties of Cowen-Douglas Class of Operators

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Parastoo Heiatian Naeini ◽  
Bahmann Yousefi
Keyword(s):  
Hilbert Space ◽  
Analytic Function ◽  
Essential Spectrum ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Multiplication Operator ◽  
Multiplication Operators ◽  
Space Of Analytic Functions ◽  
Class Operator ◽  
Necessary And Sufficient

We will consider multiplication operators on a Hilbert space of analytic functions on a domainΩ⊂C. For a bounded analytic functionφonΩ, we will give necessary and sufficient conditions under which the complement of the essential spectrum ofMφinφΩbecomes nonempty and this gives conditions for the adjoint of the multiplication operatorMφbelongs to the Cowen-Douglas class of operators. Also, we characterize the structure of the essential spectrum of a multiplication operator and we determine the commutants of certain multiplication operators. Finally, we investigate the reflexivity of a Cowen-Douglas class operator.

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