包含广义逆的算子乘积的一些不变性  

Invariance properties of a triple operator product involving generalized inverses

作　　者：陆建明[1] 高桂宝[1] 杜鸿科[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《宝鸡文理学院学报（自然科学版）》2007年第3期176-179,共4页Journal of Baoji University of Arts and Sciences(Natural Science Edition)

基　　金：国家自然科学基金(10571113)

摘　　要：目的给定3个算子A,B和C,推广了Jürgen Groβ和Yongge Tian在文献Invariance properties of a triple matrix product involving generalized inverses([1]Linear Algebra Appl,2006,417:94-107)中得到的主要结论。方法应用算子分块矩阵的技巧和解算子方程的思想进行推导,这与Jürgen Groβ和Yongge Tian的方法完全不同。结果得出了文献[1]的主要结论在无限维Hilbert空间中成立的充要条件。结论得到了与X选取无关的3个算子AXC乘积的一些不变性质,其中X是算子B的不同种类的广义逆。Aim Given three operators A, B and C, the main results obtained by Jǖrgen Groβ and Yongge Tian in ＂Invariance properties of a triple matrix product involving generalized inverses＂, （[1] Linear Algebra Appl, 2006, 417 ： 94-107） are generalized. Methods The proofs in this paper applied the technique of block operator matrix and the idea of solving operator equation. This is different from that by Jǖrgen Groβ and Yongge Tian. Results Some necessary and sufficient conditions were gotten for the main results in [1] to hold in infinite dimensional Hilbert spaces. Conclusion Certain invariance properties of the triple operator product AXC with respect to the choice of X are established, where X is a different type of generalized inverses of B.

关 键 词：广义逆 Moore—Penrose逆 值域 

分 类 号：O177.1[理学—数学]