On the Definition of C*-algebras

Abstract

It is shown that conditions $∥ x y ∥ \leq ∥ x ∥∥ y ∥$ and $∥ x^{*} ∥ = ∥ x ∥$ follow from the other axioms for $C^{*}$ -algebras.

Huzihiro Araki, George A. Elliott, On the Definition of C*-algebras. Publ. Res. Inst. Math. Sci. 9 (1973), no. 1, pp. 93–112