本文選題：可逆性 + Fredholm性�。� 參考：《內(nèi)蒙古大學(xué)》2017年碩士論文

【摘要】：本文首先綜述了算子線性組合問(wèn)題的研究背景.其次,研究了兩個(gè)閉值域算子線性組合的可逆性和Frdholm性.主要借助于空間分解的方法及算子矩陣分塊的技巧,將αA+βB化為上三角算子矩陣,利用上三角算子矩陣的可逆性和Fredholm性,分別刻畫(huà)出兩個(gè)閉值域算子4和B的線性組合是可逆算子和Fredholm算子的充分必要條件,其中α,β ∈ C\{0}.最后,給出一些特殊算子線性組合的可逆性和Fredholm性的充要條件.此外,舉例說(shuō)明了結(jié)論的有效性.
[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, 偽 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 偽, 尾 鈭，

本文編號(hào)：1748993