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

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

2009-04-06

arxiv.org/abs/0904.0893v1

J. of the Japanese Math. Soc., {\bf 60}, 511-549 (2008)

Physics

Mathematical Physics

Scientific paper

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. 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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