In this paper we show how some known quasi *-algebras can also be obtained through the construction of slight extensions of nonclosable positive linear functionals defined on dense *-subalgebras Ao of given topological *-algebras. Moreover, we consider also, for each of the functionals we present, their absolutely convergent extensions and the GNS *-representations of the quasi *-algebras arising in the process of extension.
Bellomonte, G. (2010). Quasi *-algebras arising from extensions of positive linear functionals. In Rendiconti del Circolo matematico di Palermo (pp.235-249). Palermo.
Quasi *-algebras arising from extensions of positive linear functionals
BELLOMONTE, Giorgia
2010-01-01
Abstract
In this paper we show how some known quasi *-algebras can also be obtained through the construction of slight extensions of nonclosable positive linear functionals defined on dense *-subalgebras Ao of given topological *-algebras. Moreover, we consider also, for each of the functionals we present, their absolutely convergent extensions and the GNS *-representations of the quasi *-algebras arising in the process of extension.
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