Abstract view
Generalized Dsymmetric Operators II


Published:20100819
Printed: Mar 2011
S. Bouali,
Department of Mathematics and Informatics, Faculty of Sciences Kénitra, B. P. 133 Kénitra, Morocco
M. Echchad,
Lycée mixte de Missour, 33250 Missour, Morocco
Abstract
Let $H$ be a separable,
infinitedimensional, complex Hilbert space and let $A, B\in{\mathcal L
}(H)$, where ${\mathcal L}(H)$ is the algebra of all bounded linear
operators on $H$. Let $\delta_{AB}\colon {\mathcal L}(H)\rightarrow {\mathcal
L}(H)$ denote the generalized derivation $\delta_{AB}(X)=AXXB$.
This note will initiate a study on the class of pairs $(A,B)$ such
that $\overline{{\mathcal R}(\delta_{AB})}= \overline{{\mathcal
R}(\delta_{A^{\ast}B^{\ast}})}$.
MSC Classifications: 
47B47, 47B10, 47A30 show english descriptions
Commutators, derivations, elementary operators, etc. Operators belonging to operator ideals (nuclear, $p$summing, in the Schattenvon Neumann classes, etc.) [See also 47L20] Norms (inequalities, more than one norm, etc.)
47B47  Commutators, derivations, elementary operators, etc. 47B10  Operators belonging to operator ideals (nuclear, $p$summing, in the Schattenvon Neumann classes, etc.) [See also 47L20] 47A30  Norms (inequalities, more than one norm, etc.)
