CONTINUOUS DERIVATIONS OF NONCOMMUTATIVE BANACH ALGEBRA

  • 발행 : 2000.01.01

초록

In this paper we investigate the conditions for derivations under which the Singer-Wermer theorem is true for noncommutative Banach algebra A such that either [[D(x),xD(x)] ${\in}$ rad(A) for all $x{\in}$A or $D(x)^2$x+xD(x))$^2$${\in}$rad(A) for all $x{\in}$A, where rad(A) is the Jacobson radical of A, then $D(A){\subseteq}$rad(A).

키워드

참고문헌

  1. Math. J. Okayama v.32 A note on derivations M. Bresar
  2. J. Funct. v.133 Derivations Mapping into the Radical Ⅲ
  3. Proc. Amer. Math. Soc. v.110 On left derivations and related mappings M. Bresar;J. Vukman
  4. Arch. Math. v.59 Derivations of noncommutative Banach algebras
  5. Arch. Math. v.57 Derivations mapping into the radical M. Mathieu;G. J. Murphy
  6. Proc. Amer. Math. Soc. v.20 Continuous Derivations on Banach algebras A. M. Sinclair
  7. Math. Ann. v.129 Derivations on Commutative normed algebras I. M. Singer;J. Wermer
  8. Ann. of Math. v.128 The image of a derivation is contained in the radical M. P. Thomas
  9. Pacific J. Math. v.159 Primitive ideals and derivations on non-commutative Banach algebras
  10. Glas. Mat. v.26 A result concerning derivations in noncommutative Banach algebras J. Vukman
  11. Contemp. Math. v.32 Continuous homomorphisms and derivations on Banach algebras B. Yood