Norms Of Special Elementary Operators In Standard Operator Algebra

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 define the elementary op erator where MA,B(X)=AXB,X∈A.For this elementary operator,we may defineIn this paper,we mainly study the elementary operators RA,B defined on a stan-dard operator algebra acting on a Hilbert space.We give a describe of d(RA,B).Some equivalent conditions of d(RA,B)=D(RA,B)and(I+UA,B)=D(I+UA,B)are given. Let we consider the conditions for the following inequality:d’(UA,B)≥‖A‖‖B‖.We also consider the norm of the elementary operators on standard operator algebra acting on a Banach space.