论文标题
无界操作员：（平方）根，鼻涕，可透性和一些相关的可逆性结果
Unbounded operators: (square) roots, nilpotence, closability and some related invertibility results
论文作者
论文摘要
在本文中，我们主要关注的是研究线性操作员的任意无界方形根及其一些基本属性。该论文包含许多例子和反例。作为例证，我们在任何地方都在定义的身份操作员和零操作员的无界不可碰撞的$ nth $根。我们还显示了一个不可碰撞的无界操作员，而没有任何不可碰撞的平方根。除其他后果外，我们还可以在任何地方找到定义的射击运算符，到处都有定义的操作员，这些操作员无需挪用，而无处不在的无缘算子则无需支配。还给出了一些有关鼻蛋白的相关结果。
In this paper, we are mainly concerned with studying arbitrary unbounded square roots of linear operators as well as some of their basic properties. The paper contains many examples and counterexamples. As an illustration, we give explicit everywhere defined unbounded non-closable $nth$ roots of the identity operator as well as the zero operator. We also show a non-closable unbounded operator without any non-closable square root. Among other consequences, we have a way of finding everywhere defined bijective operators, everywhere defined operators which are surjective without being injective and everywhere defined operators which are injective without being surjective. Some related results on nilpotence are also given.
