This paper is concerned with the representation problem of a coupled operator in a product space.A necessary and sufficient condition is given for a class of operators with closed range to have a one-sided coupled ope...This paper is concerned with the representation problem of a coupled operator in a product space.A necessary and sufficient condition is given for a class of operators with closed range to have a one-sided coupled operator matrix representation.The applications of this result in a delay equation and in a diffusion-transport system with dynamical boundary conditions are further presented.展开更多
Numerical range has an important applications on spectrum distribution of operators. In this paper, we devoted to characterizing operators whose numerical range contains the origin. Some necessary and sufficient condi...Numerical range has an important applications on spectrum distribution of operators. In this paper, we devoted to characterizing operators whose numerical range contains the origin. Some necessary and sufficient conditions are given by operator decomposition technique and constructive methods. Furthermore, the closeness of the numerical range of a given operator is also investigated.展开更多
This paper is concerned with general n×n upper-triangular operator matrices with given diagonal entries.The characterizations of perturbations of their left(resp.right)Weyl spectrum and Weyl spectrum are given,ba...This paper is concerned with general n×n upper-triangular operator matrices with given diagonal entries.The characterizations of perturbations of their left(resp.right)Weyl spectrum and Weyl spectrum are given,based on the space decomposition technique.Moreover,some sufficient and necessary conditions are given under which the left(resp.right)Weyl spectrum and the Weyl spectrum of such operator matrix,respectively,coincide with the union of the left(resp.right)Weyl spectrum and the Weyl spectrum of its diagonal entries.展开更多
基金Supported by the NNSF of China(Grant Nos.11961052,11761029)the Program for Innovative Research Team in Universities of Inner Mongolia Autonomous Region(Grant No.NMGIRT2317)the NSF of Inner Mongolia(Grant Nos.2021MS01006,2020ZD01)。
文摘This paper is concerned with the representation problem of a coupled operator in a product space.A necessary and sufficient condition is given for a class of operators with closed range to have a one-sided coupled operator matrix representation.The applications of this result in a delay equation and in a diffusion-transport system with dynamical boundary conditions are further presented.
基金Supported by the NNSF of China(Grant Nos.11761029,11461049,11371185,11661034 and 11761055)the NSF of Inner Mongolia(Grant No.2017MS0123)the key Science and Technology Program of Colleges and Universities of Inner Mogolia(Grant No.NJZY17234)
文摘Numerical range has an important applications on spectrum distribution of operators. In this paper, we devoted to characterizing operators whose numerical range contains the origin. Some necessary and sufficient conditions are given by operator decomposition technique and constructive methods. Furthermore, the closeness of the numerical range of a given operator is also investigated.
基金Supported by National Natural Science Foundation of China(Grant Nos.11901323 and 11961052)Natural Science Foundation of Inner Mongolia of China(Grant No.2018BS01001)+1 种基金the Research Program of Sciences at Universities of Inner Mongolia Autonomous Region(Grant Nos.NJZZ18018)SPH-IMUN(Grant No.2017YJRC018)。
文摘This paper is concerned with general n×n upper-triangular operator matrices with given diagonal entries.The characterizations of perturbations of their left(resp.right)Weyl spectrum and Weyl spectrum are given,based on the space decomposition technique.Moreover,some sufficient and necessary conditions are given under which the left(resp.right)Weyl spectrum and the Weyl spectrum of such operator matrix,respectively,coincide with the union of the left(resp.right)Weyl spectrum and the Weyl spectrum of its diagonal entries.
