### Abstract

We introduce the notion of a (noncommutative) C *-Segal algebra as a Banach algebra (A, {norm of matrix}{dot operator}{norm of matrix} A) which is a dense ideal in a C *-algebra (C, {norm of matrix}{dot operator}{norm of matrix} C), where {norm of matrix}{dot operator}{norm of matrix} A is strictly stronger than {norm of matrix}{dot operator}{norm of matrix} C onA. Several basic properties are investigated and, with the aid of the theory of multiplier modules, the structure of C *-Segal algebras with order unit is determined.

Original language | English |
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Pages (from-to) | 785-797 |

Number of pages | 13 |

Journal | Journal of Mathematical Analysis and its Applications |

Volume | 398 |

Issue number | 2 |

DOIs | |

Publication status | Published - 15 Feb 2013 |

### ASJC Scopus subject areas

- Applied Mathematics
- Analysis

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## Cite this

Kauppi, J., & Mathieu, M. (2013). C∗-Segal algebras with order unit.

*Journal of Mathematical Analysis and its Applications*,*398*(2), 785-797. https://doi.org/10.1016/j.jmaa.2012.09.031