INNER DERIVATIONS MAPPING INTO THE RADICAL

  • Published : 1998.09.01

Abstract

In this paper we show that $\sigma$a maps into the radical if and only if for every irreducible representation $\pi$,$\pi$(a) is scalar and obtain that every inner derivation corresponding to $\sigma$-quasi central elements in some Banach algebra maps into the radical.

Keywords

References

  1. A Primer on spectral theory B.Aupetit
  2. Arch. Math. Derivations decreasing the spectral radius M.Bres$\u{a}$r
  3. Proc. Amer. Math. Soc. Spectrally bounded generallize inner derivations R.Curto;M.Mathieu
  4. Where to find the image of a derivation M.Mathieu
  5. Manuscripta Math. Derivation, Commutators and the radical V.Pt$\u{a}$k
  6. J. London Math. Soc. Conditions related to centrality in a Banach algebra J.F.Rennison
  7. J. London Math. Soc. Conditions related to centrality in a Banach algebraⅡ J.F.Rennison
  8. Math. Proc. Camb. Phil. Soc. The quasi-centre of a Banach Algebra J.F.Rennison
  9. General theory of Banach algebras C.E.Ricart