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A Characterization of C*-normed Algebras via Positive Functionals

Published online by Cambridge University Press:  20 November 2018

Marina Haralampidou ,
Mohamed Oudadess ,
Lourdes Palacios  and
Carlos Signoret
Marina Haralampidou
Affiliation:
Department of Mathematics, University of Athens, Panepistimioupolis, Athens 1584, Greece, e-mail: mharalam@math.uoa.gr
Mohamed Oudadess
Affiliation:
Ecole Normale Supérieure, B.P 5118, Takaddoum, 10105 Rabat, Morocco, e-mail: oudadesshha@gmail.com
Lourdes Palacios
Affiliation:
Universidad Autónoma Metropolitana Iztapalapa, Mexico City 09340, Mexico, e-mail: pafa@xanum.uam.mx
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Abstract

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We give a characterization of ${{C}^{*}}$-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

46H0546K05C*-normed algebraC*-algebra(pre-)locally C*-algebrapre-C*-bornological algebrapositive functionallocally uniformly A-convex algebraperfect locally m-convex algebraC*-subnormable algebra*-subnormable algebra
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 61 , Issue 1 , 01 March 2018 , pp. 114 - 123
Copyright
Copyright © Canadian Mathematical Society 2018

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