Norms Of A Class Of Elementary Operators

Let A be a standard operator algebra acting on a normed space. For two n-tuples A =(A1, A2, · · ·, An), B =(B1, B2, · · ·, Bn) of elements in A, we de?ne the elementary operator RA,B=n∑i=1MAi,Bi, where MA,B(X) = AXB, X ∈ A. For this elementaryoperator, we may de?neIn this paper, we mainly study the elementary operators MA,A? + MB,B? + MC,C?de?ned on a standard operator algebra acting on a Hilbert space and give a describe of d(MA,A? + MB,B? + MC,C?). Some equivalent conditions ofand are given. We also consider the norm of the following elementary operators: I + MA?,A,δA,B, δA+ δB, δA,B+ δB,A.