Structure of locally convex quasi $C^*$-algebras
Fabio BAGARELLO, Maria FRAGOULOPOULOU, Atsushi INOUE, and Camillo TRAPANI
Source: J. Math. Soc. Japan Volume 60, Number 2
(2008), 511-549.
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.
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Keywords: quasi *-algebras; quasi-positivity; locally convex quasi $C^*$-algebras; unbounded *-representations
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Permanent link to this document: http://projecteuclid.org/euclid.jmsj/1212156661
Digital Object Identifier: doi:10.2969/jmsj/06020511
Mathematical Reviews number (MathSciNet): MR2421987
Zentralblatt MATH identifier: 1145.47059
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