The main facts about unbounded C*-seminorms on partial *-algebras are reviewed and the link with the representation theory is discussed. In particular, starting from the more familiar case of *-algebras, we examine C*-seminorms that are defined from suitable families of positive linear or sesquilinear forms, mimicking the construction of the Gelfand seminorm for Banach *-algebras. The admissibility of these forms in terms of the (unbounded) C*-seminorms they generate is characterized.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc67-0-30,
author = {Camillo Trapani},
title = {C*-seminorms on partial *-algebras: an overview},
journal = {Banach Center Publications},
volume = {68},
year = {2005},
pages = {369-384},
zbl = {1075.46045},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc67-0-30}
}
Camillo Trapani. C*-seminorms on partial *-algebras: an overview. Banach Center Publications, Tome 68 (2005) pp. 369-384. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc67-0-30/