Quasi $^*$-algebras and generalized inductive limits of $C^*$-algebras
Studia Mathematica, Tome 202 (2011) no. 2, pp. 165-190
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
A generalized procedure for the construction of the inductive limit of a family of $C^*$-algebras is proposed. The outcome is no more a $C^*$-algebra but, under certain assumptions, a locally convex quasi $^*$-algebra, named a $C^*$-inductive quasi $^*$-algebra. The properties of positive functionals and representations of $C^*$-inductive quasi $^*$-algebras are investigated, in close connection with the corresponding properties of positive functionals and representations of the $C^*$-algebras that generate the structure. The typical example of the quasi $^*$-algebra of operators acting on a rigged Hilbert space is analyzed in detail.
Keywords:
generalized procedure construction inductive limit family * algebras proposed outcome * algebra under certain assumptions locally convex quasi * algebra named * inductive quasi * algebra properties positive functionals representations * inductive quasi * algebras investigated close connection corresponding properties positive functionals representations * algebras generate structure typical example quasi * algebra operators acting rigged hilbert space analyzed detail
Affiliations des auteurs :
Giorgia Bellomonte 1 ; Camillo Trapani 1
@article{10_4064_sm202_2_4,
author = {Giorgia Bellomonte and Camillo Trapani},
title = {Quasi $^*$-algebras and generalized inductive limits of $C^*$-algebras},
journal = {Studia Mathematica},
pages = {165--190},
publisher = {mathdoc},
volume = {202},
number = {2},
year = {2011},
doi = {10.4064/sm202-2-4},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm202-2-4/}
}
TY - JOUR AU - Giorgia Bellomonte AU - Camillo Trapani TI - Quasi $^*$-algebras and generalized inductive limits of $C^*$-algebras JO - Studia Mathematica PY - 2011 SP - 165 EP - 190 VL - 202 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/sm202-2-4/ DO - 10.4064/sm202-2-4 LA - en ID - 10_4064_sm202_2_4 ER -
%0 Journal Article %A Giorgia Bellomonte %A Camillo Trapani %T Quasi $^*$-algebras and generalized inductive limits of $C^*$-algebras %J Studia Mathematica %D 2011 %P 165-190 %V 202 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/sm202-2-4/ %R 10.4064/sm202-2-4 %G en %F 10_4064_sm202_2_4
Giorgia Bellomonte; Camillo Trapani. Quasi $^*$-algebras and generalized inductive limits of $C^*$-algebras. Studia Mathematica, Tome 202 (2011) no. 2, pp. 165-190. doi: 10.4064/sm202-2-4
Cité par Sources :