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On the Range of Elementary Operators

Authors:	Salah Mecheri

Institution:	(1) College of Science, Department of Mathematics, King Saud University, P.O. Box 2455, Riyadh, 11451, Saudi Arabia

Abstract:	Let B(H) denote the algebra of all bounded linear operators on a separable infinite dimensional complex Hilbert space H into itself. Let A = (A₁,A₂,.., A_n) and B = (B₁, B₂,.., B_n) be n-tuples in B(H), we define the elementary operator $E_{A,B} : B(H) \mapsto B(H)$ by $E_{A,B} (X) = \Sigma _{i = 1}^n A_i X\,B_i.$ In this paper we initiate the study of some properties of the range of such operators.

Keywords:	Primary 47B47 47A30 47B20 Secondary 47B10
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