A characterisation of C*-algebras through positivity of functionals
Operator Algebras
2023-05-31 v2 Functional Analysis
Abstract
We show that a unital involutive Banach algebra, with identity of norm one and continuous involution, is a C*-algebra, with the given involution and norm, if every continuous linear functional attaining its norm at the identity is positive.
Keywords
Cite
@article{arxiv.1205.6830,
title = {A characterisation of C*-algebras through positivity of functionals},
author = {Marcel de Jeu and Jun Tomiyama},
journal= {arXiv preprint arXiv:1205.6830},
year = {2023}
}
Comments
3 pages. Some typos corrected. Final version, to appear in Ann. Funct. Anal