On the product of two generalized derivations
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- by Mohamed Barraa and Steen Pedersen PDF
- Proc. Amer. Math. Soc. 127 (1999), 2679-2683 Request permission
Abstract:
Two elements $A$ and $B$ in a ring $\mathfrak {R}$ determine a generalized derivation $\delta _{A,B}$ on $\mathfrak {R}$ by setting $\delta _{A,B}(X)$ $=AX-XA$ for any $X$ in $\mathfrak {R}$. We characterize when the product $\delta _{C,D}\delta _{A,B}$ is a generalized derivation in the cases when the ring $\mathfrak {R}$ is the algebra of all bounded operators on a Banach space $\mathcal {E}$, and when $\mathfrak {R}$ is a $C^{*}$–algebra $\mathfrak {A}$. We use these characterizations to compute the commutant of the range of $\delta _{A,B}$.References
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Additional Information
- Mohamed Barraa
- Affiliation: Departement de Mathematiques, Faculte des Sciences–Semlalia, University Cadi Ayyad, B.P.: S. 15, 40000 Marrakech, Marocco
- Steen Pedersen
- Affiliation: Department of Mathematics, Wright State University, Dayton, Ohio 45435
- MR Author ID: 247731
- Email: steen@math.wright.edu
- Received by editor(s): December 30, 1996
- Received by editor(s) in revised form: November 20, 1997
- Published electronically: April 15, 1999
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 2679-2683
- MSC (1991): Primary 47B47, 46L40
- DOI: https://doi.org/10.1090/S0002-9939-99-04899-6
- MathSciNet review: 1610904