#### Document Type

Article

#### Publication Date

9-1997

#### Abstract

Two elements *A* and *B* in a ring **R** determine a generalized derivation delta* _{A,B}* on

**R**by setting δ

_{A,B}

*(X)*=

*AX - XA*for any

*X*in

**R**. We characterize when the product δ

*δ*

_{C,D}_{A,B}is a

*generalized derivation*in the cases when the ring

**R**is the algebra of all bounded operators on a Banach space epsilon, and when

**R**is a

*C**-algebra

**U**. We use the se characterizations to compute the commutant of the range of δ

_{A,B}.

#### Repository Citation

Barraa, M.,
& Pedersen, S.
(1997). On the Product of Two Generalized Derivations. *Proceedings of the American Mathematical Society, 127* (9), 2679-2683.

https://corescholar.libraries.wright.edu/math/18

#### DOI

10.1090/S0002-9939-99-04899-6

## Comments

First published in

Proceedings of the American Mathematical Society127.9 (1999), published by the American Mathematical Society.