Fully representable and $^*$-semisimple topological partial $^*$-algebras
Studia Mathematica, Tome 208 (2012) no. 2, pp. 167-194
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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 $\mathcal M$-bounded elements introduced in previous works.
Keywords:
continue study topological partial * algebras focusing attention * semisimple partial * algebras those possess multiplication core sufficiently many * representations discuss respective roles invariant positive sesquilinear ips forms representable continuous linear functionals focus where notions completely interchangeable fully representable partial * algebras characterizing * semisimple partial * algebra finally describe various notions bounded elements partial * algebra particular those defined terms positive cone order bounded elements outcome appropriate order relation recovers mathcal m bounded elements introduced previous works
Affiliations des auteurs :
J.-P. Antoine 1 ; G. Bellomonte 2 ; C. Trapani 2
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author = {J.-P. Antoine and G. Bellomonte and C. Trapani},
title = {Fully representable and $^*$-semisimple topological partial $^*$-algebras},
journal = {Studia Mathematica},
pages = {167--194},
publisher = {mathdoc},
volume = {208},
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year = {2012},
doi = {10.4064/sm208-2-4},
language = {en},
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J.-P. Antoine; G. Bellomonte; C. Trapani. Fully representable and $^*$-semisimple topological partial $^*$-algebras. Studia Mathematica, Tome 208 (2012) no. 2, pp. 167-194. doi: 10.4064/sm208-2-4
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