Vol. 50, No. 2, 1974

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The range of a derivation and ideals

Robert Earl Weber

Vol. 50 (1974), No. 2, 617–624
Abstract

When A is in the Banach algebra () of all bounded linear operators on a Hilbert space , the derivation generated by A is the bounded operator ΔA on () defined by Δ4(X) = AX XA. It is shown that the range of a derivation generated by a Hilbert-Schmidt or a diagonal operator contains no nonzero one-sided ideals of (). Also, for a two.sided ideal of (), necessary and sufficient condition on an operator A are given in order that the range of ΔA equals the range of ΔA restricted to .

Mathematical Subject Classification 2000
Primary: 47B10
Milestones
Received: 28 November 1972
Revised: 10 October 1973
Published: 1 February 1974
Authors
Robert Earl Weber