Definition 2

For every element $x$ of a normed algebra A, the real number

$\varrho (x) =$ lim$_{n\rightarrow \infty}\|x^n\|^{1/n}=$ inf$_{n>0}\|x^n\|^{1/n}$

is called the spectral radius of $x$.

For every element $x$ of A, one has

(4) $\varrho (x^n) =\varrho (x)^n$, for every integer $n\geqslant 1$.