### Abstract

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

pagine (da-a) | 2973-2980 |

Numero di pagine | 8 |

Rivista | Proceedings of the American Mathematical Society |

Volume | 129 |

Stato di pubblicazione | Published - 2001 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cita questo

*Proceedings of the American Mathematical Society*,

*129*, 2973-2980.

**Some classes of topological quasi *-algebras.** / Trapani, Camillo; Bagarello, Fabio; Inoue.

Risultato della ricerca: Article

*Proceedings of the American Mathematical Society*, vol. 129, pagg. 2973-2980.

}

TY - JOUR

T1 - Some classes of topological quasi *-algebras

AU - Trapani, Camillo

AU - Bagarello, Fabio

AU - Inoue, null

PY - 2001

Y1 - 2001

N2 - The completion A[τ] of a locally convex *-algebra A[τ] with not jointly continuous multiplication is a *-vector space with partial multiplication xy defined only for x or y ε A0, and it is called a topological quasi *-algebra. In this paper two classes of topological quasi *-algebras called strict CQ*-algebras and HCQ*-algebras are studied. Roughly speaking, a strict CQ*-algebra (resp. HCQ*-algebra) is a Banach (resp. Hubert) quasi *-algebra containing a C*-algebra endowed with another involution # and C*norm || ||#. HCQ*-algebras are closely related to left Hubert algebras. We shall show that a Hubert space is a HCQ*-algebra if and only if it contains a left Hubert algebra with unit as a dense subspace. Further, we shall give a necessary and sufficient condition under which a strict CQ*-aIgebra is embedded in a HCQ*-algebra. © 2001 American Mathematical Society.

AB - The completion A[τ] of a locally convex *-algebra A[τ] with not jointly continuous multiplication is a *-vector space with partial multiplication xy defined only for x or y ε A0, and it is called a topological quasi *-algebra. In this paper two classes of topological quasi *-algebras called strict CQ*-algebras and HCQ*-algebras are studied. Roughly speaking, a strict CQ*-algebra (resp. HCQ*-algebra) is a Banach (resp. Hubert) quasi *-algebra containing a C*-algebra endowed with another involution # and C*norm || ||#. HCQ*-algebras are closely related to left Hubert algebras. We shall show that a Hubert space is a HCQ*-algebra if and only if it contains a left Hubert algebra with unit as a dense subspace. Further, we shall give a necessary and sufficient condition under which a strict CQ*-aIgebra is embedded in a HCQ*-algebra. © 2001 American Mathematical Society.

UR - http://hdl.handle.net/10447/195460

M3 - Article

VL - 129

SP - 2973

EP - 2980

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

ER -