| 董 炯,曹小红.算子矩阵值域的闭性及其应用[J].数学年刊A辑,2020,41(4):383~298 |
| 算子矩阵值域的闭性及其应用 |
| Closedness of Ranges for Operator Matrices and Its Application |
| 投稿时间：2019-05-14 修订日期：2020-07-05 |
| DOI：10.16205/j.cnki.cama.2020.0027 |
| 中文关键词: 值域, 半Fredholm算子, 算子矩阵, 广义Weyl算子 |
| 英文关键词:Range, Semi-Fredholm operator, Operator matrix, Generalized Weyl operator |
| 基金项目:国家自然科学基金(No.11471200, No.11701351)和陕西省自然科学基础研究(No.2018JQ1082) |
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| 中文摘要: |
| 令{H}和{K}均为无限复可分的Hilbert空间. 定义MX=(A&CX&B)为作用在{H}}oplus{K}上的2x2算子矩阵, 其中X为从{H}到{K}上未知的有界线性算子.在本文中, 基于R(C)的闭性对某个(或任意的)Xin{B}}({H,K}}), 使得R(M_{X})为闭集的充要条件做了等价刻画.另外, 研究了算子矩阵M_{X的半Fredholm性与广义Weyl性并给出了一些相应的结论. |
| 英文摘要: |
| Let H and K be infinite dimensional separable complex Hilbert spaces. The authors denote by MX = A C X B a 2 × 2 operator matrix acting on H ⊕ K, where X is an unknown bounded linear operator from H to K. In this paper, based on the closedness of R(C), the authors characterize the necessary and sufficient condition for R(MX) to be closed for some (or every) X ∈ B(H, K). In addition, the authors study the semi-Fredholmness and generalized Weylness of MX and give some relevant results. |
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