Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지

LINEAR DERIVATIONS IN BANACH ALGEBRAS

  • Published : 2001.08.01
Download PDF
⟨ Previous Next ⟩

Abstract

The main goal of this paper is to show the following: Let d and g be (continuous or discontinuous) linear derivations on a Banach algebra A over a complex field C such that $\alphad^3+dg$ is a linear Jordan derivation for some $\alpha\inC$. Then the product dg maps A into the Jacobson radical of A.

Keywords

References

  1. Proc. Amer. Math. Soc. v.104 Jordan derivations on semiprime rings M. Bresar
  2. J. London Math. Soc. v.16 no.2 Automatic continuity and topologically simple radical Banach algebras J. Cusack
  3. Bull. London Math. Soc. v.24 Derivations mapping into the radical Ⅱ M. Mathieu;V. Runde
  4. Proc. Amer. Math. Soc. v.8 Derivations in prime rings E. Posner
  5. London Math. Soc. Lecture Note Ser. v.21 Automatic continuity of linear operators A. M. Sinclair
  6. Math. Ann. v.129 Derivations on commutative normed algebras I. M. Singer;J. Wermer
  7. Ann. of Math. v.128 The image of a derivation is contained in the radical M. P. Thomas
  8. Pacific J. Math v.159 Primitive ideals and derivations on non-commutative Banach algebras M. P. Thomas
  9. Proc. Amer. Math. Soc. v.116 A result concerning derivations in Banach algebras J. Vukman