Spectrum of an element
= Spectrum of an element
{title2=$\sigma_A(a)$}
= Banach algebra spectrum
{c}
{synonym}
= Banach algebra spectra
{c}
{synonym}
= Algebra spectrum
{synonym}
= Algebra spectra
{synonym}
The spectrum of $a$ in a unital complex algebra $A$ is
$$
\sigma_A(a)=\{\lambda\in\mathbb C:a-\lambda1\text{ is not invertible}\}.
$$
For a nonunital algebra it is defined in the <unitization of an algebra>.