The class of *-representations of a normed quasi *-algebra (𝔛,𝓐₀) is investigated, mainly for its relationship with the structure of (𝔛,𝓐₀). The starting point of this analysis is the construction of GNS-like *-representations of a quasi *-algebra (𝔛,𝓐₀) defined by invariant positive sesquilinear forms. The family of bounded invariant positive sesquilinear forms defines some seminorms (in some cases, C*-seminorms) that provide useful information on the structure of (𝔛,𝓐₀) and on the continuity properties of its *-representations.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm186-1-6,
author = {Camillo Trapani},
title = {*-Representations, seminorms and structure properties of normed quasi *-algebras},
journal = {Studia Mathematica},
volume = {187},
year = {2008},
pages = {47-75},
zbl = {1151.46037},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm186-1-6}
}
Camillo Trapani. *-Representations, seminorms and structure properties of normed quasi *-algebras. Studia Mathematica, Tome 187 (2008) pp. 47-75. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm186-1-6/