论文标题
积极的Hankel操作员，积极的确定内核和相关主题
Positive Hankel operators, positive definite kernels and related topics
论文作者
论文摘要
结果表明，具有微不足道内核的希尔伯特空间上的正（有限线性）算子在单位上等同于汉克尔操作员，当且仅当它是不可变形且具有简单频谱的情况下，该操作员满足双重阳性条件（也就是说，如果该操作员允许一个循环向量）。更笼统地，对于具有微不足道内核的Hilbert空间H上的任意正（有限线性）算子A的收集V（a）的所有线性异构体V（a）从H到H的所有线性异构体V（a），因此AV也是阳性的。特别是，v（a）包含具有给定缺陷指数的纯轴测图。提出了一些用于无界积极的自我伴侣运算符以及积极确定内核的应用。特别是，研究了此类内核的正定矩阵型正方形根，并且具有独特的词根的核是特征的。还研究了至少一个这样的平方根的所有正定核的类别。
It is shown that a positive (bounded linear) operator on a Hilbert space with trivial kernel is unitarily equivalent to a Hankel operator that satisfies double positivity condition if and only if it is non-invertible and has simple spectrum (that is, if this operator admits a cyclic vector). More generally, for an arbitrary positive (bounded linear) operator A on a Hilbert space H with trivial kernel the collection V(A) of all linear isometries V from H into H such that AV is positive as well is investigated. In particular, operators A such that V(A) contains a pure isometry with a given deficiency index are characterized. Some applications to unbounded positive self-adjoint operators as well as to positive definite kernels are presented. In particular, positive definite matrix-type square roots of such kernels are studied and kernels that have a unique such root are characterized. The class of all positive definite kernels that have at least one such a square root is also investigated.
