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.

在有限维空间上，很明显，当且仅当与正算子相似时，算子才是两个正算子的乘积。在这里，研究可分离的无限维希尔伯特空间上有界算子的类\（{\ mathcal {L} ^ {+ \，2}} \\），它可以写成两个有界正算子的乘积。结构要丰富得多，并且将（但不等同于）准相似性和准亲和性连接到一个正算子。运营商在光谱特性\（{\ mathcal {L} ^ {+ \，2}} \）的开发，并且在隶属\（{\ mathcal {L} ^ {+ \，2}} \）中特别检查包括代数和紧致算子的类。