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victorballester7 committed Dec 1, 2023
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\begin{definition}
Let $H$ be a $\KK$-Hilbert space and $K:H\to H$ be a compact operator. We define the \emph{resolvent set} of $K$ as:
$$
\rho(K)=\{\lambda\in \KK: \lambda-K \text{ is invertible}\}
\rho(K)=\{\lambda\in \KK: \lambda\id-K \text{ is invertible}\}
$$
and the \emph{spectrum} of $K$ as:
$$
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