A model space is a subspace of the Hardy space which is invariant under the backward shift,and a truncated Toeplitz operator is the compression of a Toeplitz operator on some model space.In this paper we prove a neces...A model space is a subspace of the Hardy space which is invariant under the backward shift,and a truncated Toeplitz operator is the compression of a Toeplitz operator on some model space.In this paper we prove a necessary and sufficient condition for the commutator of two truncated Toeplitz operators on a model space to be compact.展开更多
In this paper,the authors completely characterize when two dual truncated Toeplitz operators ar e essentially commuting and when the semicommutator of two dual truncated Toeplitz operators is compact.Their main idea i...In this paper,the authors completely characterize when two dual truncated Toeplitz operators ar e essentially commuting and when the semicommutator of two dual truncated Toeplitz operators is compact.Their main idea is to study dual truncated Toeplitz operators via Hankel operators,Toeplitz operators and function algebras.展开更多
We investigate some problems for truncated Toeplitz operators. Namely, the solvability of the Riccati operator equation on the set of all truncated Toeplitz operators on the model space Kθ = H^2θθH^2 is studied. We...We investigate some problems for truncated Toeplitz operators. Namely, the solvability of the Riccati operator equation on the set of all truncated Toeplitz operators on the model space Kθ = H^2θθH^2 is studied. We study in terms of Berezin symbols invertibility of model operators. We also prove some results for the Berezin number of the truncated Toeplitz operators. Moreover, we study some property for H2-functions in terms of noncyclicity of co-analytic Toeplitz operators and hypercyclicity of model operators.展开更多
文摘A model space is a subspace of the Hardy space which is invariant under the backward shift,and a truncated Toeplitz operator is the compression of a Toeplitz operator on some model space.In this paper we prove a necessary and sufficient condition for the commutator of two truncated Toeplitz operators on a model space to be compact.
基金supported by the National Natural Science Foundation of China(Nos.11531003,12371125)the Fundamental Research Funds for the Central Universities(Nos.2020CDJQY-A039,2020CDJ-LHSS-003)。
文摘In this paper,the authors completely characterize when two dual truncated Toeplitz operators ar e essentially commuting and when the semicommutator of two dual truncated Toeplitz operators is compact.Their main idea is to study dual truncated Toeplitz operators via Hankel operators,Toeplitz operators and function algebras.
文摘We investigate some problems for truncated Toeplitz operators. Namely, the solvability of the Riccati operator equation on the set of all truncated Toeplitz operators on the model space Kθ = H^2θθH^2 is studied. We study in terms of Berezin symbols invertibility of model operators. We also prove some results for the Berezin number of the truncated Toeplitz operators. Moreover, we study some property for H2-functions in terms of noncyclicity of co-analytic Toeplitz operators and hypercyclicity of model operators.
