scholarly journals Semicommutators and Zero Product of Block Toeplitz Operators with Harmonic Symbols

2013 ◽  
Vol 2013 ◽  
pp. 1-4
Author(s):  
Puyu Cui ◽  
Yufeng Lu ◽  
Yanyue Shi
Keyword(s):  
Bergman Space ◽  
Finite Rank ◽  
Toeplitz Operators ◽  
Block Toeplitz Operators ◽  
Vector Valued

We completely characterize the finite rank semicommutators, commutators, and zero product of block Toeplitz operatorsTFandTGwithF,G∈h∞⊗Mn×non the vector valued Bergman spaceLa2(𝔻,ℂn).

scholarly journals Algebraic Properties of Toeplitz Operators on the Pluriharmonic Bergman Space

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Jingyu Yang ◽  
Liu Liu ◽  
Yufeng Lu
Keyword(s):  
Toeplitz Operator ◽  
Bergman Space ◽  
Finite Rank ◽  
Toeplitz Operators ◽  
Sufficient Conditions ◽  
Rank Product ◽  
Algebraic Properties ◽  
Necessary And Sufficient ◽  
Product Problem ◽  
Quasihomogeneous Symbols

We study some algebraic properties of Toeplitz operators with radial or quasihomogeneous symbols on the pluriharmonic Bergman space. We first give the necessary and sufficient conditions for the product of two Toeplitz operators with radial symbols to be a Toeplitz operator and discuss the zero-product problem for several Toeplitz operators with radial symbols. Next, we study the finite-rank product problem of several Toeplitz operators with quasihomogeneous symbols. Finally, we also investigate finite rank commutators and semicommutators of two Toeplitz operators with quasihomogeneous symbols.

scholarly journals Algebraic Properties of Toeplitz Operators on the Polydisk

2011 ◽  
Vol 2011 ◽  
pp. 1-18 ◽  
Author(s):  
Bo Zhang ◽  
Yanyue Shi ◽  
Yufeng Lu
Keyword(s):  
Bergman Space ◽  
Finite Rank ◽  
Toeplitz Operators ◽  
Rank Product ◽  
Algebraic Properties ◽  
Product Problem ◽  
Quasihomogeneous Symbols

We discuss some algebraic properties of Toeplitz operators on the Bergman space of the polydiskDn. Firstly, we introduce Toeplitz operators with quasihomogeneous symbols and property (P). Secondly, we study commutativity of certain quasihomogeneous Toeplitz operators and commutators of diagonal Toeplitz operators. Thirdly, we discuss finite rank semicommutators and commutators of Toeplitz operators with quasihomogeneous symbols. Finally, we solve the finite rank product problem for Toeplitz operators on the polydisk.

scholarly journals Toeplitz Operators with Quasihomogeneous Symbols on the Bergman Space of the Unit Ball

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Bo Zhang ◽  
Yufeng Lu
Keyword(s):  
Unit Ball ◽  
Toeplitz Operator ◽  
Bergman Space ◽  
Finite Rank ◽  
Toeplitz Operators ◽  
Quasihomogeneous Symbols

We consider when the product of two Toeplitz operators with some quasihomogeneous symbols on the Bergman space of the unit ball equals a Toeplitz operator with quasihomogeneous symbols. We also characterize finite-rank semicommutators or commutators of two Toeplitz operators with quasihomogeneous symbols.

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