On the range-kernel orthogonality of elementary operators
On the range-kernel orthogonality of elementary operators
Let $L(H)$ denote the algebra of operators on a complex infinite dimensional Hilbert space $H$. For $A, B\in L(H)$, the generalized derivation $\delta _{A,B}$ and the elementary operator $\Delta _{A,B}$ are defined by $\delta _{A,B}(X)=AX-XB$ and $\Delta _{A,B}(X)=AXB-X$ for all $X\in L(H)$. In this paper, we exhibit pairs $(A,B)$ of …