Definition 4

One says that $\widetilde{A}$, endowed with the norm of Prop. 3, is the star algebra deduced from A by adjunction of a unit element.

When $A\not=\{0\}$, the norm of star algebra on the normed involutive algebra $\widetilde{A}$ is not the one considered in Example 6 of I, p. 101 (cf. Exercise 10 of I, p. 181).