Solution
= Solution
For a <bounded linear operator> on a complex <Banach space>, its <spectrum> is
$$
\boxed{\sigma(T)=\{\lambda\in\mathbb C:\lambda I-T
\text{ has no bounded two-sided inverse}\}.}
$$
The complement is the <resolvent set>. For a real space, one may use its complexification when speaking of the complex <spectrum>; the algebraic arguments below apply over the underlying scalar field as well.