Truncation and spectral variation in Banach algebras

C. Touré, F. Schulz, R. Brits

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


Let a and b be elements of a semisimple, complex and unital Banach algebra A. Using subharmonic methods, we show that if the spectral containment σ(ax)⊆σ(bx) holds for all x∈A, then ax belongs to the bicommutant of bx for all x∈A. Given the aforementioned spectral containment, the strong commutation property then allows one to derive, for a variety of scenarios, a precise connection between a and b. The current paper gives another perspective on the implications of the above spectral containment which was also studied, not long ago, by J. Alaminos, M. Brešar et al.

Original languageEnglish
Pages (from-to)23-31
Number of pages9
JournalJournal of Mathematical Analysis and Applications
Issue number1
Publication statusPublished - 1 Jan 2017


  • C-algebra
  • Spectral radius
  • Spectrum
  • Subharmonic
  • Truncation

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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