DERIVATIONS ON NONCOMMUTATIVE BANACH ALGEBRAS

  • Published : 2000.01.01

Abstract

It is well-known that every derivation on a commutative Banach algebra maps into its radical. In this paper we shall give the various algebraic conditions on the ring that every Jordan derivation on a noncommutative ring with suitable characteristic conditions is zero and using this result, we show that every continuous linear Jordan derivation on a noncommutative Banach algebra maps into its radical under the suitable conditions.

Keywords

References

  1. Complete normed algebras F.F.Bonsall;J. Duncan
  2. Arch. Math. v.59 Derivations of noncommutative Banach algebras M. Bresar;J. Vukman
  3. Math. J. Okayama Univ. v.32 A note on derivations M. Bresar
  4. Bull. Austral. Math. Soc. v.47 On skew-commuting mapping of rings
  5. Proc. Math. Soc. v.104 Jordan derivations on semiprime rings
  6. Ph. D. Thesis Derivations on semiprime rings and Banach algebras S. H. Byun
  7. Canad. Math. Bull. v.24 no.4 Semiprime rings with nilpotent derivations L. O. Chung;J. Luh
  8. Amer. Math Soc. v.8 Jordan derivations on prime rings I. N. Herstein
  9. Amer. J. Math. v.91 Continuity of derivations on commutative Banach algebras B. E. Johnson
  10. Kangwon Kyungki Math. J. v.3 no.1 Derivation of prime ring and Banach algebras B. D. Kim
  11. Proc. Amer. Math. v.8 Derivations in prime rings E. Posner
  12. Studia Math. v.105 no.2 Range inclusion results for derivations on noncommutative Banach algebras V. Runde
  13. Proc. Amer. Math. Soc. v.24 Jordan homomorphisms and derivations on semisimple Banach algebras A. M. Sinclair
  14. Math. Amer. v.129 Derivations on commutative normed algebras A. M. Singer;J. Wermer
  15. Bull. Austral. Math. Soc. v.53 Derivations in semiprime rings J. Vukman
  16. Amer of Math. v.128 The image of a derivation is contained in the radical M. P. Thomas
  17. Proc. Amer. Math. Soc. v.116 On derivations in prime and Banach algebras
  18. Glasnik. Math. v.26 A result concerning derivations in noncommutative Banach algebras
  19. Proc. Amer. Math. Soc. v.109 Commuting and centralizing mappings in prime rings
  20. Contemp. Math. v.32 Continuous homomorphisms and derivation on Banach algebras B. Yood