arXiv subjects
Publications and source records attributed to Maria Fragoulopoulou.
Quasi *-algebras form an essential class of partial *-algebras, which are algebras of unbounded operators. In this work, we aim to construct tensor products of normed, respectively Banach quasi *-algebras, and study their capacity to preserve some important properties of their tensor factors, like for instance, *-semisimplicity and full representability.
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.