In this paper we consider the block Toeplitz operators TФ on the weighted Bergman space A2α（D, Cn） and we give a necessary and sufficient condition for the hyponor-mality of block Toeplitz operators with symbol in...In this paper we consider the block Toeplitz operators TФ on the weighted Bergman space A2α（D, Cn） and we give a necessary and sufficient condition for the hyponor-mality of block Toeplitz operators with symbol in the class of functions Ф=F ＋ G＊ withmatrix-valued polynomial functions F and G with degree 2.展开更多
We consider the hyponormality of the block dual Toeplitz operator S_(Φ)acting on the orthogonal complement of the vector valued weighted Bergman space (A_(α)^(2)(D,C^(n)))^(⊥).We provide a necessary and sufficient ...We consider the hyponormality of the block dual Toeplitz operator S_(Φ)acting on the orthogonal complement of the vector valued weighted Bergman space (A_(α)^(2)(D,C^(n)))^(⊥).We provide a necessary and sufficient condition for the hyponormality of SΦwith matrix valued bounded harmonic symbol.In this process,we introduce a function g_(w,s)∈(A_(α)^(2)(D))^(⊥),which is similar to the reproducing kernel of the weighted Bergman space A_(α)^(2)(D).We also give some additional applications of the function gw,s∈(A_(α)^(2)(D))^(⊥).展开更多
In this paper,we characterize the boundedness and compactness of the block dual Toeplitz operators acting on the orthogonal complement of the Fock spaces,and the compactness of the finite sum of two dual Toeplitz oper...In this paper,we characterize the boundedness and compactness of the block dual Toeplitz operators acting on the orthogonal complement of the Fock spaces,and the compactness of the finite sum of two dual Toeplitz operators products.The commutator and semi-commutator induced by the block dual Toeplitz operators are considered.展开更多
基金supported by Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education(2009-0093827)
文摘In this paper we consider the block Toeplitz operators TФ on the weighted Bergman space A2α（D, Cn） and we give a necessary and sufficient condition for the hyponor-mality of block Toeplitz operators with symbol in the class of functions Ф=F ＋ G＊ withmatrix-valued polynomial functions F and G with degree 2.
基金Supported by the Scientific Research Fund of Liaoning Provincial Education Department of China (Grant No.LJKMZ20221405)the National Natural Science Foundation of China (Grant No.12031002)。
文摘We consider the hyponormality of the block dual Toeplitz operator S_(Φ)acting on the orthogonal complement of the vector valued weighted Bergman space (A_(α)^(2)(D,C^(n)))^(⊥).We provide a necessary and sufficient condition for the hyponormality of SΦwith matrix valued bounded harmonic symbol.In this process,we introduce a function g_(w,s)∈(A_(α)^(2)(D))^(⊥),which is similar to the reproducing kernel of the weighted Bergman space A_(α)^(2)(D).We also give some additional applications of the function gw,s∈(A_(α)^(2)(D))^(⊥).
文摘In this paper,we characterize the boundedness and compactness of the block dual Toeplitz operators acting on the orthogonal complement of the Fock spaces,and the compactness of the finite sum of two dual Toeplitz operators products.The commutator and semi-commutator induced by the block dual Toeplitz operators are considered.
