Exercise 8, § 2

Let A be the algebra of continuous complex functions on $\mathbf{R}$ tending to 0 at infinity, equipped with the norm $\|f\|=$ sup$_{t\in\mathbf{R}}|f(t)|$. Then $\widetilde{A}$ is identified with the algebra of continuous complex functions on $\mathbf{R}$ tending to a finite limit at infinity. On $\widetilde{A}$, the norm $\|g\|=$ sup$_{t\in\mathbf{R}}|g(t)|$ differs from the norm defined at No$^o1$ of I, p. 15.