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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
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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
MSC Classifications: 46H05, 46K05 show english descriptions General theory of topological algebras
General theory of topological algebras with involution
46H05 - General theory of topological algebras
46K05 - General theory of topological algebras with involution
 

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