Some classes of topological quasi *-algebras

dc.creatorBagarello, F.
dc.creatorInoue, A.
dc.creatorTrapani, C.
dc.date2009-04-06
dc.date.accessioned2026-07-07T13:00:48Z
dc.date.available2026-07-07T13:00:48Z
dc.descriptionThe completion $\overline{A}[τ]$ of a locally convex *-algebra $A [ τ]$ with not jointly continuous multiplication is a *-vector space with partial multiplication $xy$ defined only for $x$ or $y \in A_{0}$, and it is called a topological quasi *-algebra. In this paper two classes of topological quasi *-algebras called strict CQ$^*$-algebras and HCQ$^*$-algebras are studied. Roughly speaking, a strict CQ$^*$-algebra (resp. HCQ$^*$-algebra) is a Banach (resp. Hilbert) quasi *-algebra containing a C$^*$-algebra endowed with another involution $\sharp$ and C$^*$-norm $\| \|_{\sharp}$. HCQ$^*$-algebras are closely related to left Hilbert algebras. We shall show that a Hilbert space is a HCQ$^*$-algebra if and only if it contains a left Hilbert algebra with unit as a dense subspace. Further, we shall give a necessary and sufficient condition under which a strict CQ$^*$-algebra is embedded in a HCQ$^*$-algebra.
dc.identifierhttps://arxiv.org/abs/0904.0892
dc.identifierhttp://arxiv.org/abs/0904.0892
dc.identifierProc. Amer. Math. Soc., 129, 2973-2980 (2001)
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/225958
dc.subjectMathematical Physics
dc.titleSome classes of topological quasi *-algebras
dc.typetext

Files

Collections