### Abstract

This paper starts from noting that, under certain conditions, *-representability andextensibility to the unitized *-algebra of a positive linear functional, defined on a *-algebra without unit,are equivalent. Here some conditions for the equivalence of the same concepts for a hermitian linearfunctional defined on a quasi *-algebra $(\A,\Ao)$ without unit are given. The approach is twofold: onthe one hand, conditions for the equivalence are exhibited by introducing a condition for the *-representability of the extension of a *-representable functional to the unitized quasi *-algebra, on theother hand a *-representable extension to the unitization of a hermitian linear functional by means of aclosable invariant sesquilinear form is constructed.

Lingua originale | English |
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pagine (da-a) | 1461-1473 |

Numero di pagine | 13 |

Rivista | Mediterranean Journal of Mathematics |

Volume | 10 |

Stato di pubblicazione | Published - 2013 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)