Spectrally bounded φ-derivations on Banach algebras

Tsiu Kwen Lee, Cheng Kai Liu

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


Applying the density theorem on algebras with φ-derivations, we show that if a φ-derivation δ of a unital Banach algebra A is spectrally bounded, then [δ(A), A] ⊆ rad(A). Also, δ(A) ⊆ rad(A) if and only if sup{r(z-1δ(z)) | z ε A is invertible} < ∞, where r(a) denotes the spectral radius of a ε A.

Original languageEnglish
Pages (from-to)1427-1435
Number of pages9
JournalProceedings of the American Mathematical Society
Issue number5
Publication statusPublished - 2005 May

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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