Fully representable and *-semisimple topological partial *-algebras

J.-P. Antoine, G. Bellomonte, and C. Trapani. "Fully representable and *-semisimple topological partial *-algebras." Studia Mathematica 208.2 (2012): 167-194. <http://eudml.org/doc/285434>.

@article{J2012,
abstract = {We continue our study of topological partial *-algebras, focusing our attention on *-semisimple partial *-algebras, that is, those that possess a multiplication core and sufficiently many *-representations. We discuss the respective roles of invariant positive sesquilinear (ips) forms and representable continuous linear functionals, and focus on the case where the two notions are completely interchangeable (fully representable partial *-algebras) with the aim of characterizing a *-semisimple partial *-algebra. Finally we describe various notions of bounded elements in such a partial *-algebra, in particular, those defined in terms of a positive cone (order bounded elements). The outcome is that, for an appropriate order relation, one recovers the ℳ-bounded elements introduced in previous works.},
author = {J.-P. Antoine, G. Bellomonte, C. Trapani},
journal = {Studia Mathematica},
keywords = {topological partial -algebras; -semisimple partial -algebras; bounded elements},
language = {eng},
number = {2},
pages = {167-194},
title = {Fully representable and *-semisimple topological partial *-algebras},
url = {http://eudml.org/doc/285434},
volume = {208},
year = {2012},
}

TY - JOUR
AU - J.-P. Antoine
AU - G. Bellomonte
AU - C. Trapani
TI - Fully representable and *-semisimple topological partial *-algebras
JO - Studia Mathematica
PY - 2012
VL - 208
IS - 2
SP - 167
EP - 194
AB - We continue our study of topological partial *-algebras, focusing our attention on *-semisimple partial *-algebras, that is, those that possess a multiplication core and sufficiently many *-representations. We discuss the respective roles of invariant positive sesquilinear (ips) forms and representable continuous linear functionals, and focus on the case where the two notions are completely interchangeable (fully representable partial *-algebras) with the aim of characterizing a *-semisimple partial *-algebra. Finally we describe various notions of bounded elements in such a partial *-algebra, in particular, those defined in terms of a positive cone (order bounded elements). The outcome is that, for an appropriate order relation, one recovers the ℳ-bounded elements introduced in previous works.
LA - eng
KW - topological partial -algebras; -semisimple partial -algebras; bounded elements
UR - http://eudml.org/doc/285434
ER -