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
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, 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.
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.
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.
