Multiplicative maps into the spectrum

Cheick Touré, Francois Schulz, Rudi Brits

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


We consider the converse of a famous result of W. Żelazko et al. which characterizes multiplicative functionals amongst the dual space members of a complex unital Banach algebra A. Specifically, we investigate when a continuous multiplicative map φ: A → ℂ, with values φ(x) belonging to the spectrum of x, is automatically linear. Our main result states that if A is a C-algebra, then φ always generates a corresponding character φ of A. It is then shown that φ shares many linear properties with its induced character. Moreover, if A is a von Neumann algebra, then it turns out that φ itself is linear, and that it corresponds to its induced character.

Original languageEnglish
Pages (from-to)55-66
Number of pages12
JournalStudia Mathematica
Issue number1
Publication statusPublished - 2017


  • C-algebra
  • Linear functional
  • Multiplicative functional
  • Spectrum
  • Von Neumann Algebra

ASJC Scopus subject areas

  • General Mathematics


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