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The commutant of Analytic Toeplitz Operators on Bergman Space

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Acta Mathematica Sinica,English Series 2008年第10期24卷 1737-1750页

作者： Yu Cheng LI Department of Mathematics Hebei Normal University Shijiazhuang 050016 P. R. China

In this paper, using the matrix skills and operator theory techniques we characterize the commutant of analytic Toeplitz operators on Bergman space. For f（z） = z^ng（z）（n ≥1）, g（z） = b0 ＋ b1z^p1 ＋b2z^p2 ＋.. , bk ≠ 0 （k = 0, 1, 2,...）, our main result is =A′（Mf） = A′（Mzn）∩A′（Mg） = A′（Mz^s）, where s = g.c.d.（n,p1,p2,...）. In the last section, we study the relation between strongly irreducible curve and the winding number W（f,f（α））, α ∈ D.

关键词： Bergman space analytic Toeplitz operator commutant strong irreducibility

The commutant and similarity invariant of analytic Toeplitz operators on Bergman space

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Science China Mathematics 2007年第5期50卷 651-664页

作者： Chun-Ian JIANG Yu-cheng Li Department of Mathematics Hebei Normal UniversityShijiazhuang 050016China

The famous von Neumann-Wold Theorem tells us that each analytic Toeplitz operator with n + 1-Blaschke factors is unitary to n + 1 copies of the unilateral shift on the Hardy space. It is obvious that the von Neumann-Wold Theorem does not hold in the Bergman space. In this paper, using the basis constructed by Michael and Zhu on the Bergman space we prove that each analytic Toeplitz operator Mb(z) is similar to n + 1 copies of the Bergman shift if and only if B(z) is an n + 1-Blaschke product. Prom the above theorem, we characterize the similarity invariant of some analytic Toeplitz operators by using K0-group term.

关键词： Bergman space analytic Toeplitz operators invariant subspace commutant similarity invariant K0-group

A new C~*-algebra and its essential commutant

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Chinese Science Bulletin 1999年第3期44卷 204-207页

作者： Jinshan Liu Yunxin Zhang Kunyu Guo Fudan Univ Inst Math Shanghai 200433 Peoples R China

A new C~* -algebra E+E_* is established. It contains the large Hankel algebra N^G produced by all Toeplitz operators and Hankel operators. It is the proper algebra of B (H^2) and its essential commutant is obtained, which is generated by those Toeplitz operators that have symmetric continuous function symbols and compact operators.

关键词： essential commutant Toeplitz operator Hankel operator.

Bn（Ω）中一类新的完全酉不变量和加权双边位移的换位子

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Northeastern Mathematical Journal 1994年第3期10卷 401-410页

作者：严从荃

In this paper, we give a new comPlete set of unitary invariants for an operator T in the Cowen-Douglas class a(Ω), and therefore provide a new way of studying this class.A sufficient and necessary condition for a wei... 详细信息

关键词： Cowen-Doglas Class Completely Unitary Invariant Weighted Unilateral Shift Operator commutant

Reducing subspaces of multiplication operators on function spaces

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Applied Mathematics(A Journal of Chinese Universities) 2013年第4期28卷 395-404页

作者： GUO Kun-yu HUANG Han-song School of Mathematical Sciences Fudan University Department of Mathematics East China University of Science and Technology

This survey presents the brief history and recent development on commutants and reducing subspaces of multiplication operators on both the Hardy space and the Bergman space, and von Neumann algebras generated by multi... 详细信息

关键词： reducing subspace commutant von Neumann algebra Blaschke product holomorphic covering map

THE FIELD ALGEBRA IN HOPF SPIN MODELS DETERMINED BY A HOPF*-SUBALGEBRA AND ITS SYMMETRIC STRUCTURE

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Acta Mathematica Scientia 2021年第3期41卷 907-924页

作者：魏晓敏蒋立宁辛巧玲 School of Mathematics and Statistics Beijing Institute of TechnologyBeijing 100081China School of Mathematical Sciences Tianjin Normal UniversityTianjin 300387China

Denote a finite dimensional Hopf C*-algebra by H, and a Hopf *-subalgebra of H by H1. In this paper, we study the construction of the field algebra in Hopf spin models determined by H1 together with its symmetry. More precisely, we consider the quantum double D(H, H_(1)) as the bicrossed product of the opposite dual Hopˆ of H and H1 with respect to the coadjoint representation, the latter acting on the former and vice versa, and under the non-trivial commutation relations between H1 and Ĥ we define the observable algebra AH1. Then using a comodule action of D(H, H1) on AH1, we obtain the field algebra FH1, which is the crossed product AH1⋊D(H,H_(1)), and show that the observable algebra AH1 is exactly a D(H, H1)-invariant subalgebra of FH1. Furthermore, we prove that there exists a duality between D(H, H1) and AH1, implemented by a*-homomorphism of D(H, H_(1)).

关键词： Comodule algebra field algebra observable algebra commutant duality

About Operator Weighted Shift

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Acta Mathematica Sinica,English Series 2007年第8期23卷 1385-1390页

作者： Chun Lan JIANG Yong Fei JIN Zong Yao WANG Department of Mathematics Hebei Normal University Shifiazhuang 050016 P. R. China Department of Mathematics East China University of Science and Technology Shanghai 200237 P. R. China

Abstract Let H be a complex seperable Hilbert space and ^（Jt^） denote the collection of bounded linear operators on H. For an operator in L（H）, rad{A}＇ denotes the Jacobson radical of the commutant of A. This paper characterizes the similarity of strongly irreducible operator weighted shift in terms of {A}＇/rad{A}＇. Moreover, we suggest some ways to determine when an operator weighted shift is strongly irreducible and when its commutant is commutative.

关键词： Operator weighted shift Strongly irriducible operator Similarity commutant Jacobson radical

The commutants of analytic Toeplitz operators for several complex variables

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Science China Mathematics 2010年第7期53卷 1873-1880页

作者： Cao GuangFu Huang Sui Guangzhou Univ Dept Math Guangzhou 510006 Guangdong Peoples R China

It is proved that if  is a nonconstant bounded analytic function on the unit ball B n and continuous on S n in C n , and ψ is a bounded measurable function on S n such that T * and T ψ commute, then ψ is the boundary value of an analytic function on B n . In addition, the commutants of two Toeplitz operators are also discussed.

关键词： Toeplitz operator commutant of an operator

Commuting of Toeplitz Operators in Several Complex Variables

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Northeastern Mathematical Journal 2001年第3期17卷 253-256页

作者：卢玉峰孙善利 DepartmentofAppliedMathematics DalianUniversityofTechnologyDalian160024 CommunicatedbySunShanli

1 IntroductionLet Ω be the unit ball Bn or the polydisk Dn in Cn, and dA denote the Lebesgue measure on Ω, normalized so that the measure of Ω equals 1. L2a(Ω) is The Bergman space. For z ∈Ω, the Bergman reprodu... 详细信息

关键词： Toeplitz operator commutant function of several complex variables