We investigate the Furi-Martelli-Vignoli spectrum and the Feng spectrum of continuous nonlinear block operator matrices,and mainly describe the relationship between the Furi-Martelli-Vignoli spectrum(compared to the F...We investigate the Furi-Martelli-Vignoli spectrum and the Feng spectrum of continuous nonlinear block operator matrices,and mainly describe the relationship between the Furi-Martelli-Vignoli spectrum(compared to the Feng spectrum)of the whole operator matrix and that of its entries.In addition,the connection between the Furi-Martelli-Vignoli spectrum of the whole operator matrix and that of its Schur complement is presented by means of Schur decomposition.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 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
In this paper,some refinements of norm equalities and inequalities of combination of two orthogonal projections are established.We use certain norm inequalities for positive contraction operator to establish norm ineq...In this paper,some refinements of norm equalities and inequalities of combination of two orthogonal projections are established.We use certain norm inequalities for positive contraction operator to establish norm inequalities for combination of orthogonal projections on a Hilbert space.Furthermore,we give necessary and sufficient conditions under which the norm of the above combination of o`rthogonal projections attains its optimal value.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
In this paper, the adjoint of a densely defined block operator matrix L=[A B C D] in a Hilbert space X ×X is studied and the sufficient conditions under which the equality L＊=[A＊ B＊ C＊ D＊] holds are obtained...In this paper, the adjoint of a densely defined block operator matrix L=[A B C D] in a Hilbert space X ×X is studied and the sufficient conditions under which the equality L＊=[A＊ B＊ C＊ D＊] holds are obtained through applying Frobenius-Schur factorization.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11561048 and 11761029)the Natural Science Foundation of Inner Mongolia,China(Grant Nos.2019MS01019 and 2020ZD01)。
文摘We investigate the Furi-Martelli-Vignoli spectrum and the Feng spectrum of continuous nonlinear block operator matrices,and mainly describe the relationship between the Furi-Martelli-Vignoli spectrum(compared to the Feng spectrum)of the whole operator matrix and that of its entries.In addition,the connection between the Furi-Martelli-Vignoli spectrum of the whole operator matrix and that of its Schur complement is presented by means of Schur decomposition.
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))^(⊥).
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.
文摘In this paper,some refinements of norm equalities and inequalities of combination of two orthogonal projections are established.We use certain norm inequalities for positive contraction operator to establish norm inequalities for combination of orthogonal projections on a Hilbert space.Furthermore,we give necessary and sufficient conditions under which the norm of the above combination of o`rthogonal projections attains its optimal value.
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.
基金Supported by NSFC(Grant Nos.11101200,11371185,2013ZD01)
文摘In this paper, the adjoint of a densely defined block operator matrix L=[A B C D] in a Hilbert space X ×X is studied and the sufficient conditions under which the equality L＊=[A＊ B＊ C＊ D＊] holds are obtained through applying Frobenius-Schur factorization.
