Products of Diagonal Operators

Let X be a separable complex Hilbert space, B(X)the set of all (bounded linear)operators acting on X. For T∈B(X), the question whether T can be factorized into the product of some good operators has been discussed by many authors (e. g. Ref. [1]—[6]). In [1], Wu obtained some sufficient and necessary conditions for an operator to be a prod-