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On the distance of the composition of two derivations to the generalized derivations

  • Matej Bresar (a1)
  • DOI: http://dx.doi.org/10.1017/S0017089500008077
  • Published online: 01 May 2009
Abstract

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.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

1.J. Bergen , I. N. Herstein and J. Kerr , Lie ideals and derivations of prime rings, J. Algebra 71 (1981), 259267.

3.C. K. Fong and A. R. Sourour , On the operator identity ΣAkXBk ≡ = 0, Canad. J. Math. 31 (1979), 845857.

4.P. Gajendragadkar , Norm of a derivation on a von Neumann algebra, Trans. Amer. Math. Soc. 170 (1972), 165170.

5.C. Lanski , Differential identities, Lie ideals, and Posner's theorems, Pacific J. Math. 134 (1988), 275297.

7.M. Mathieu , Elementary operators on prime C*-algebras I, Math. Ann. 284 (1989), 223244.

10.E. Posner , Derivations in prime rings, Proc. Amer. Math. Soc. 8 (1957), 10931100.

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

12.J. P. Williams , On the range of a derivation, Pacific J. Math. 38 (1971), 273279.

13.L. Zsidó , The norm of a derivation in a W*-algebra, Proc. Amer. Math. Soc. 38 (1973), 147150.

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Glasgow Mathematical Journal
  • ISSN: 0017-0895
  • EISSN: 1469-509X
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