论文标题
在$ \ ast $ rings中的一些广义倒置和部分订单上
On some generalized inverses and partial orders in $\ast$-rings
论文作者
论文摘要
令$ \ Mathcal {r} $为一个有偶然性的Unital环。 1MP Inverse和Mp1 inverse的概念从$ M_ {M，N}（\ Mathbb {C）} $，这是所有$ \ Mathbb {c} $上的所有$ M \ times n $矩阵的集合的集合，以$ \ mathbb {c} $，以下$ \ MATHCAL {R} $。我们研究由1MP Invers和MP1 Invers引起的$ \ Mathcal {R}^{\ Dagger} $的部分订单。我们还扩展到Rickart $ \ ast $ -ring的设置，该概念是另一部分订单的概念，称为Plus Order，最近在Hilbert Space之间的所有有界线性运算符的集合中引入了该订单。研究了这些关系的特性，因此已知一些已知结果。
Let $\mathcal{R}$ be a unital ring with involution. The notions of 1MP-inverse and MP1-inverse are extended from $M_{m,n}(\mathbb{C)}$, the set of all $m\times n $ matrices over $\mathbb{C}$, to the set $\mathcal{R}% ^{\dagger}$ of all Moore-Penrose invertible elements in $\mathcal{R}$. We study partial orders on $\mathcal{R}^{\dagger}$ that are induced by 1MP-inverses and MP1-inverses. We also extend to the setting of Rickart $\ast $-rings the concept of another partial order, called the plus order, which has been recently introduced on the set of all bounded linear operators between Hilbert spaces. Properties of these relations are investigated and some known results are thus generalized.
