Range kernel orthogonality of derivations Original Research Article

Let H be a separable infinite dimensional complex Hilbert space, and let B(H) denote the algebra of operators on H into itself. The generalised derivation δA,B:B(H)→B(H) is defined by δA,B(X)=AX−XB; let up triangle, openA,B:B(H)→B(H) be defined by up triangle, openA,B(X)=AXB−X, and let dA,B denote δA,B or up triangle, openA,B. Let image (the Schatten p-class, 1