## Journal of the Mathematical Society of Japan

### Structure of locally convex quasi $C^*$-algebras

#### Abstract

The completion of a (normed) $C^*$-algebra $\A_0[\| \cdot \|_0]$  with respect to a locally convex topology $\tau$  on $\A_0$ that makes the multiplication of $\A_0$  separately continuous is, in general, a quasi $*$-algebra, and not a locally convex $*$-algebra [10], [15]. In this way, one is led to consideration of locally convex quasi $C^*$-algebras, which generalize $C^*$-algebras in the context of quasi $*$-algebras. Examples are given and the structure of these relatives of $C^*$-algebras is investigated.

#### Article information

Source
J. Math. Soc. Japan Volume 60, Number 2 (2008), 511-549.

Dates
First available in Project Euclid: 30 May 2008

http://projecteuclid.org/euclid.jmsj/1212156661

Digital Object Identifier
doi:10.2969/jmsj/06020511

Mathematical Reviews number (MathSciNet)
MR2421987

Zentralblatt MATH identifier
1145.47059

#### Citation

BAGARELLO, Fabio; FRAGOULOPOULOU, Maria; INOUE, Atsushi; TRAPANI, Camillo. Structure of locally convex quasi C * -algebras. Journal of the Mathematical Society of Japan 60 (2008), no. 2, 511--549. doi:10.2969/jmsj/06020511. http://projecteuclid.org/euclid.jmsj/1212156661.

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