Splitting of Operators and Operator Equations

In this paper,we consider the splitting operators into the product of two positive operators.For given operators A and T ∈ B(H) with A≥0 and ■,if T can be splitted as T=AX for some positive operator X,then the existence of X and the properties of T are studied.The related research are the solutions of operator equations T=XAX and TX=XAX,which have some particular properties and broad applications in many fields.The conditions for the existence of solutions or idempotent solutions of these kinds ...