Abstract view
A characterization of $C^{\ast}$normed algebras via positive functionals


Marina Haralampidou,
Department of Mathematics, University of Athens, Panepistimioupolis, Athens 15784, Greece
Mohamed Oudadess,
Ecole Normale Supérieure, B.P 5118, Takaddoum, 10105 Rabat, Morocco
Lourdes Palacios,
Universidad Autónoma Metropolitana Iztapalapa, Mexico City 09340, Mexico
Carlos Signoret,
Universidad Autónoma Metropolitana Iztapalapa, Mexico City 09340, Mexico
Abstract
We give a characterization of $C^{\ast}$normed algebras, among
certain involutive normed ones. This is done through the existence
of enough specific positive functionals. The same question is
also
examined in some non normed (topological) algebras.
Keywords: 
$C^{\ast}$normed algebra, $C^*$algebra, (pre)locally $C^*$algebra, pre$C^*$bornological algebra, positive functional, locally uniformly $A$convex algebra, perfect locally $m$convex algebra, $C^*$(resp. $^*$) subnormable algebra
$C^{\ast}$normed algebra, $C^*$algebra, (pre)locally $C^*$algebra, pre$C^*$bornological algebra, positive functional, locally uniformly $A$convex algebra, perfect locally $m$convex algebra, $C^*$(resp. $^*$) subnormable algebra
