1207.2015 (Fabio Bagarello et al.)

Locally convex quasi $C^*$-normed algebras    [PDF]

Fabio Bagarello, Maria Fragoulopoulou, Atsushi Inoue, Camillo TRapani

If $\ca_0[|\cdot|_0]$ is a $\cs$-normed algebra and $\tau$ a locally convex topology on $\ca_0$ making its multiplication separately continuous, then $\widetilde{\ca_0}[\tau]$ (completion of $\ca_0[\tau]$) is a locally convex quasi *-algebra over $\ca_0$, but it is not necessarily a locally convex quasi *-algebra over the $\cs$-algebra $\widetilde{\ca_0}[|\cdot|_0]$ (completion of $\ca_0[|\cdot|_0]$). In this article, stimulated by physical examples, we introduce the notion of a locally convex quasi $\cs$-normed algebra, aiming at the investigation of $\widetilde{\ca_0}[\tau]$; in particular, we study its structure, *-representation theory and functional calculus.

View original: http://arxiv.org/abs/1207.2015