Geodesic
Generalized D-symmetric Operators II
Canadian mathematical bulletin, Tome 54 (2011) no. 1, pp. 21-27

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DOI

Let $H$ be a separable, infinite-dimensional, complex Hilbert space and let $A,\,B\,\in \,\mathcal{L}\left( H \right)$ , where $\mathcal{L}(H)$ is the algebra of all bounded linear operators on $H$ . Let ${{\delta }_{AB}}\,:\mathcal{L}\left( H \right)\to \mathcal{L}\left( H \right)$ denote the generalized derivation ${{\delta }_{AB}}\left( X \right)\,=\,AX\,-\,XB$ . This note will initiate a study on the class of pairs $\left( A,\,B \right)$ such that $\overline{R\left( {{\delta }_{AB}} \right)}\,=\,\overline{R\left( {{\delta }_{A*\,B*}} \right)}$ .
DOI : 10.4153/CMB-2010-094-2
Mots-clés : 47B47, 47B10, 47A30, generalized derivation, adjoint, D-symmetric operator, normal operator 
Bouali, S.; Ech-chad, M. Generalized D-symmetric Operators II. Canadian mathematical bulletin, Tome 54 (2011) no. 1, pp. 21-27. doi: 10.4153/CMB-2010-094-2
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     title = {Generalized {D-symmetric} {Operators} {II}},
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     pages = {21--27},
     year = {2011},
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     doi = {10.4153/CMB-2010-094-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2010-094-2/}
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