Geodesic
Generalized D-Symmetric Operators I
Serdica Mathematical Journal, Tome 34 (2008) no. 3, pp. 557-562.

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Let H be an infinite-dimensional complex Hilbert space and let A, B ∈ L(H), where L(H) is the algebra of operators on H into itself. Let δAB: L(H) → L(H) denote the generalized derivation δAB(X) = AX − XB. This note will initiate a study on the class of pairs (A,B) such that [‾(R(δAB))] = [‾(R(δB*A*))]; i.e. [‾(R(δAB))] is self-adjoint.
Keywords: Generalized Derivation, Self-Adjoint Derivation Ranges, D-Symmetric Operators 
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     title = {Generalized {D-Symmetric} {Operators} {I}},
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Bouali, S.; Ech-chad, M. Generalized D-Symmetric Operators I. Serdica Mathematical Journal, Tome 34 (2008) no. 3, pp. 557-562. http://geodesic.mathdoc.fr/item/SMJ2_2008_34_3_a2/