关于初等算子∑(X):AX+XB+CDX的值域

摘要

Let A, B, C and D be compact operators acting on a Hilbert space H. Define ∑(X) = AX + XB + CXD for X ∈ B(H). In this paper, we give several conditions(sufficientor necessary) such that the range of ∑ is closed.%设A,B和C是Hilbert空间H上的紧算子,定义B(H)上的初等算子:∑(x)=AX+XB+CXD.本文我们给出∑值域闭的一些充分或必要条件.