论文标题
彼此伴随的操作员的范围内核表征
Range-kernel characterizations of operators which are adjoint of each other
论文作者
论文摘要
我们为希尔伯特太空运营商的一对，t $ t $提供必要的条件，以使他们满足$ s^*= t $和$ t $ and $ t^*= s $。作为主要结果，我们建立了冯·诺伊曼（Von Neumann）的古典定理，即两个变量的$ s^*s $的积极自我相关性。我们还给出了一些新的自我婚前和偏差的特征，而不是分别需要其对称性或偏斜对称。
We provide necessary and sufficient conditions for a pair $S,T$ of Hilbert space operators in order that they satisfy $S^*=T$ and $T^*=S$. As a main result we establish an improvement of von Neumann's classical theorem on the positive self-adjointness of $S^*S$ for two variables. We also give some new characterizations of self-adjointness and skew-adjointness of operators, not requiring their symmetry or skew-symmetry, respectively.
