Geodesic
Derivations from Hereditary Subalgebras of C*-Algebras
Canadian journal of mathematics, Tome 38 (1986) no. 1, pp. 109-126

Voir la notice de l'article provenant de la source Cambridge University Press

Let A be a C*-algebra, B a C*-subalgebra of A, δ:B → A a derivation, i.e., a linear map with There has been considerable interest for several years now in the question of when δ can be extended from B to a derivation of A (see, for example, [8], Section 4, [1], [5], [4], [6], [9], [10], [11]). The paper before the reader will be concerned with this extension problem when B is a hereditary C*-subalgebra of A.Our work takes its cue from the paper [6] of George Elliott. We prove in Section 2 of the present paper that derivations as described above of a unital hereditary C*-subalgebra always extend whenever A is either simple, AW*, separable and AF, or separable with continuous trace, thus generalizing and extending Theorem 4.5 of [6]. 
Lazar, A. J.; Tsui, S.-K.; Wright, S. Derivations from Hereditary Subalgebras of C*-Algebras. Canadian journal of mathematics, Tome 38 (1986) no. 1, pp. 109-126. doi: 10.4153/CJM-1986-006-5
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