论文标题
积极对称操作员和凯林独特标准的扩展
Extensions of positive symmetric operators and Krein's uniqueness criteria
论文作者
论文摘要
我们修改了Kerin的积极对称操作员的扩展理论。我们通过辅助希尔伯特空间进行分解的方法具有多个优点：它可以应用于非定义的转换，并且在真实和复杂的空间中起作用。作为结果和构造的应用，我们考虑了模量正方形操作员的积极自我偶相扩展，该构成密集定义的线性转换$ t $的$ t^*t $以及对称操作员的有界自动化扩展。凯林（Kerin）关于正（分别保存规范）自我偶极性扩展的独特性的结果也得到了修改。
We revise Krein's extension theory of positive symmetric operators. Our approach using factorization through an auxiliary Hilbert space has several advantages: it can be applied to non-densely defined transformations and it works in both real and complex spaces. As an application of the results and the construction we consider positive self-adjoint extensions of the modulus square operator $T^*T$ of a densely defined linear transformation $T$ and bounded self-adjoint extensions of a symmetric operator. Krein's results on the uniqueness of positive (respectively, norm preserving) self-adjoint extensions are also revised.
