算子线性组合的可逆性与Fredholm性

发布时间：2018-04-14 11:00

  本文选题：可逆性 + Fredholm性　； 参考：《内蒙古大学》2017年硕士论文

【摘要】：本文首先综述了算子线性组合问题的研究背景.其次,研究了两个闭值域算子线性组合的可逆性和Frdholm性.主要借助于空间分解的方法及算子矩阵分块的技巧,将αA+βB化为上三角算子矩阵,利用上三角算子矩阵的可逆性和Fredholm性,分别刻画出两个闭值域算子4和B的线性组合是可逆算子和Fredholm算子的充分必要条件,其中α,β ∈ C\{0}.最后,给出一些特殊算子线性组合的可逆性和Fredholm性的充要条件.此外,举例说明了结论的有效性.
[Abstract]:In this paper, the research background of operator linear combination problem is reviewed.Secondly, the reversibility and Frdholm property of linear combination of two closed range operators are studied.By means of the method of space decomposition and the technique of dividing operator matrix into blocks, 伪 A 尾 B is transformed into upper triangular operator matrix, and the reversibility and Fredholm property of upper triangular operator matrix are used.The sufficient and necessary conditions for the linear combination of two closed range operators 4 and B to be invertible operators and Fredholm operators are described respectively, where 伪, 尾 鈭，

本文编号：1748993