## Abstract

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 language | English |
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Pages (from-to) | 55-66 |

Number of pages | 12 |

Journal | Studia Mathematica |

Volume | 239 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2017 |

## Keywords

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

## ASJC Scopus subject areas

- General Mathematics