On the product of two generalized derivations

Authors:
Mohamed Barraa and Steen Pedersen

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

Published electronically:
April 15, 1999

MathSciNet review:
1610904

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Abstract | References | Similar Articles | Additional Information

Abstract: Two elements and in a ring determine a generalized derivation on by setting for any in . We characterize when the product is a *generalized derivation* in the cases when the ring is the algebra of all bounded operators on a Banach space , and when is a -algebra . We use these characterizations to compute the commutant of the range of .

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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

Email:
steen@math.wright.edu

DOI:
https://doi.org/10.1090/S0002-9939-99-04899-6

Keywords:
Derivation,
generalized derivation,
elementary operator,
$C^{*}$--algebra

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

Article copyright:
© Copyright 1999
American Mathematical Society