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中文摘要：
目的：给定3个算子A，B和C，推广了Jǖrgen 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方程的思想进行推导，这与Jǖrgen 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。
英文摘要：
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.
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