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The range of a
derivation and ideals
Robert Earl Weber |
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Vol. 50 (1974), No. 2, 617–624
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Abstract |
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When A is in the Banach algebra ℬ(ℋ) of all bounded linear operators on a Hilbert space ℋ, the derivation generated by A is the bounded operator ΔA on ℬ(ℋ) 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 ℬ(ℋ). Also, for a two.sided ideal ℐ of ℬ(ℋ), necessary and sufficient condition on an operator A are given in order that the range of ΔA equals the range of ΔA restricted to ℐ. |
Mathematical Subject Classification 2000
Primary: 47B10
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Milestones
Received: 28 November 1972
Revised: 10 October 1973
Published: 1 February 1974
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Authors |
| Robert Earl Weber | |
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