A characterisation of C*-algebras through positivity of functionals

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.

3 pages. Some typos corrected. Final version, to appear in Ann. Funct. Anal

Cited by in corpus (1)

• Deformation of involution and multiplication in a C*-algebra