论文标题
1MP和MP1倒置和一个环中的单方面恒星订单
1MP and MP1 inverses and one-sided star orders in a ring with involution
论文作者
论文摘要
最近引入了复杂矩阵的广义对倒置类别的1MP内和MP1内的类。实际上，它们与$ \ {1,2,3 \} $和$ \ {1,2,4 \} $ iNverses的类相吻合。我们认为这些倒在环的背景下，并证明它们最重要的特征和属性仍然是正确的。我们表明，基于这些逆的二进制关系实际上是众所周知的左星和右星部分订单。我们将这些关系扩展到环形情况，将它们与基于广义倒置的部分秩序关系的统一理论联系起来，并提供多种属性。最后，我们指出如何将这些结果应用于有限的希尔伯特太空运营商。
The classes of 1MP-inverses and MP1-inverses are recently introduced classes of generalized inverses of complex matrix. Actually, they coincide with the classes of $\{1,2,3\}$ and $\{1,2,4\}$ inverses, respectively. We consider these inverses in the context of a ring with involution and prove that their most important characterizations and properties remain true. We show that the binary relations based on these inverses are in fact the well known left-star and right-star partial orders. We extend these relations to the ring case, connect them with the unified theory of partial order relations based on generalized inverses and provide several properties. Finally, we indicate how these results can be applied to bounded Hilbert space operators.
