Geodesic
On the distance of the composition of two derivations to the generalized derivations
Glasgow mathematical journal, Tome 33 (1991) no. 1, pp. 89-93

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

A well-known theorem of E. Posner [10] states that if the composition d1d2 of derivations d1d2 of a prime ring A of characteristic not 2 is a derivation, then either d1 = 0 or d2 = 0. A number of authors have generalized this theorem in several ways (see e.g. [1], [2], and [5], where further references can be found). Under stronger assumptions when A is the algebra of all bounded linear operators on a Banach space (resp. Hilbert space), Posner's theorem was reproved in [3] (resp. [12]). Recently, M. Mathieu [8] extended Posner's theorem to arbitrary C*-algebras. 
Bresar, Matej. On the distance of the composition of two derivations to the generalized derivations. Glasgow mathematical journal, Tome 33 (1991) no. 1, pp. 89-93. doi: 10.1017/S0017089500008077
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[1] 1.Bergen, J., Herstein, I. N. and Kerr, J., Lie ideals and derivations of prime rings, J. Algebra 71 (1981), 259–267. Google Scholar | DOI

[2] 2.Brěsar, M. and Vukman, J., Orthogonal derivations and an extension of a theorem of Posner, to appear in Rad. Mat. Google Scholar

[3] 3.Fong, C. K. and Sourour, A. R., On the operator identity ΣAXB ≡ = 0, Canad. J. Math. 31 (1979), 845–857. Google Scholar | DOI

[4] 4.Gajendragadkar, P., Norm of a derivation on a von Neumann algebra, Trans. Amer. Math. Soc. 170 (1972), 165–170. Google Scholar | DOI

[5] 5.Lanski, C., Differential identities, Lie ideals, and Posner's theorems, Pacific J. Math. 134 (1988), 275–297. Google Scholar

[6] 6.Mathieu, M., Applications of ultraprime Banach algebras in the theory of elementary operators, Thesis (Tübingen, 1986). Google Scholar

[7] 7.Mathieu, M., Elementary operators on prime C*-algebras I, Math. Ann. 284 (1989), 223–244. Google Scholar | DOI

[8] 8.Mathieu, M., Properties of the product of two derivations of a C*-algebra, to appear in Canad. Math. Bull. Google Scholar

[9] 9.Mathieu, M., Rings of quotients of ultraprime Banach algebras. With applications to elementary operators, to appear in the Proceedings of the Conference on Banach algebras and Automatic Continuity (Canberra, Australia, 1989). Google Scholar

[10] 10.Posner, E., Derivations in prime rings, Proc. Amer. Math. Soc. 8 (1957), 1093–1100. Google Scholar | DOI

[11] 11.Sakai, S., C*-algebras and W*-algebras (Springer-Verlag, 1971). Google Scholar

[12] 12.Williams, J. P., On the range of a derivation, Pacific J. Math. 38 (1971), 273–279. Google Scholar | DOI

[13] 13.Zsidó, L., The norm of a derivation in a W*-algebra, Proc. Amer. Math. Soc. 38 (1973), 147–150. Google Scholar

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