@article {15211,
	title = {Rank one operators and norm of elementary operators},
	journal = {Linear Algebra Appl.},
	volume = {424},
	year = {2007},
	pages = {177-183},
	abstract = {Let A be a standard operator algebra acting on a (real or complex) normed space E. For two n-tuplesA = (A1, . . . , An) and B = (B1, . . . , Bn) of elements in A, we define the elementary operator RA,B onA by the relation RA,B(X) = ni=1 AiXBi for all X in A. For a single operator A ∈ A, we define thetwo particular elementary operators LA and RA onAby LA(X) = AX and RA(X) = XA, for every X inA. We denote by d(RA,B) the supremum of the norm of RA,B(X) over all unit rank one operators on E.In this note, we shall characterize: (i) the supremun d(RA,B), (ii) the relation d(RA,B) = ni=1AiBi,(iii) the relation d(LA- RB) = A + B, (iv) the relation d(LARB+ LBRA) = 2AB. Moreover,we shall showthe lower estimate d(LA- RB)  max{supλ∈V (B)A - λI, supλ∈V (A)B - λI} (whereV (X) is the algebraic numerical range of X inA).},
	author = {Seddik. A}
}
