Exercise 21, § 2

Let A be a unital normed algebra. Let B be the normed algebra $\mathscr{L}(A)$. Then the image of A by the morphism $x\mapsto \boldsymbol{\gamma }_x$ is a full subalgebra of B. Thus, if $x\in A$, we have Sp$_A(x) =$ Sp$_B(\boldsymbol{\gamma }_x)$.