### Abstract

Lingua originale | English |
---|---|

pagine (da-a) | 357-376 |

Numero di pagine | 20 |

Rivista | JOURNAL OF OPERATOR THEORY |

Volume | 56 |

Stato di pubblicazione | Published - 2006 |

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### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

### Cita questo

*JOURNAL OF OPERATOR THEORY*,

*56*, 357-376.

**The completion of a C*-algebra with a locally convex topology.** / Trapani, Camillo; Bagarello, Fabio; Fragoulopoulou, Maria; Inoue, Atsushi.

Risultato della ricerca: Article

*JOURNAL OF OPERATOR THEORY*, vol. 56, pagg. 357-376.

}

TY - JOUR

T1 - The completion of a C*-algebra with a locally convex topology

AU - Trapani, Camillo

AU - Bagarello, Fabio

AU - Fragoulopoulou, Maria

AU - Inoue, Atsushi

PY - 2006

Y1 - 2006

N2 - There are examples of C*-algebras A that accept a locally convex*-topology t coarser than the given one, such that Ae[t] (the completion ofA with respect to t) is a GB*-algebra. The multiplication of A[t] may be ornot be jointly continuous. In the second case, Ae[t] may fail being a locallyconvex *-algebra, but it is a partial *-algebra. In both cases the structure andthe representation theory of Ae[t] are investigated. If A[t+]denotes the t-closureof the positive cone A+ of the given C*-algebra A, then the property A[t]+\cap (−A[t]+) = {0} is decisive for the existence of certain faithful *-representationsof the corresponding *-algebra Ae[t].

AB - There are examples of C*-algebras A that accept a locally convex*-topology t coarser than the given one, such that Ae[t] (the completion ofA with respect to t) is a GB*-algebra. The multiplication of A[t] may be ornot be jointly continuous. In the second case, Ae[t] may fail being a locallyconvex *-algebra, but it is a partial *-algebra. In both cases the structure andthe representation theory of Ae[t] are investigated. If A[t+]denotes the t-closureof the positive cone A+ of the given C*-algebra A, then the property A[t]+\cap (−A[t]+) = {0} is decisive for the existence of certain faithful *-representationsof the corresponding *-algebra Ae[t].

KW - GB-algebra

KW - Partial -algebra

KW - Unbounded C-seminorm

UR - http://hdl.handle.net/10447/12475

M3 - Article

VL - 56

SP - 357

EP - 376

JO - JOURNAL OF OPERATOR THEORY

JF - JOURNAL OF OPERATOR THEORY

SN - 0379-4024

ER -