论文标题
积极运营商的产品
Products of positive operators
论文作者
论文摘要
在有限的维空间上，很明显，当且仅当它与正运算符相似时，操作员是两个正运算符的产物。在这里，在可分离的无限尺寸希尔伯特空间上，有界运算符的类$ {\ Mathcal l}^{+2} $可以写入两个有界正算子的乘积。该结构要富裕得多，并且与正算子连接（但不等于）准相似性和准亲和力。开发了$ {\ Mathcal L}^{+2} $中运算符的光谱属性，并检查了包括代数和紧凑型操作员在内的特殊类中的$ {\ Mathcal l}^{+2} $中的成员资格。
On finite dimensional spaces, it is apparent that an operator is the product of two positive operators if and only if it is similar to a positive operator. Here, the class ${\mathcal L}^{+2}$ of bounded operators on separable infinite dimensional Hilbert spaces which can be written as the product of two bounded positive operators is studied. The structure is much richer, and connects (but is not equivalent to) quasi-similarity and quasi-affinity to a positive operator. The spectral properties of operators in ${\mathcal L}^{+2}$ are developed, and membership in ${\mathcal L}^{+2}$ among special classes, including algebraic and compact operators, is examined.
