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arXiv · 1207.2015

Locally convex quasi $C^*$-normed algebras

Fabio Bagarello·Maria Fragoulopoulou·Atsushi Inoue·Camillo TRapani
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Abstract

If $\ca_0[|\cdot|_0]$ is a $\cs$-normed algebra and $τ$ a locally convex topology on $\ca_0$ making its multiplication separately continuous, then $\widetilde{\ca_0}[τ]$ (completion of $\ca_0[τ]$) 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 $\widetilde{\ca_0}[τ]$; in particular, we study its structure, *-representation theory and functional calculus.

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BibTeXRIS

Fabio Bagarello, Maria Fragoulopoulou, Atsushi Inoue, Camillo TRapani. 2012-07-09. Locally convex quasi $C^*$-normed algebras. https://arxiv.org/abs/1207.2015

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