Commit a6a49f13 authored by Jannes Bantje's avatar Jannes Bantje

updated todo!

parent 753db117
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......@@ -456,7 +456,7 @@ To finally prove the Fredholm property we need the following result from functio
Let $U,V,W$ be Hilbert spaces, $D \colon U \to V$ bounded and $\K \colon U \to W$ compact.
Assume that there is a constant $C$ with
\[
\norm*{u}_U \le C \enbrace*{\norm*{D u}_V + \norm*{K u}_W}
\norm*{u}_U \le C \enbrace[\big]{\norm*{D u}_V + \norm*{K u}_W}
\]
Then the kernel of $D$ is finite dimensional and $D$ has closed image.
\end{proposition}
......@@ -532,5 +532,5 @@ Using functional calculus \cref{thm:elliptic_spectral} easily gives the followin
If $\varphi \in C_0(\mathbb{R})$ the operator $\varphi(D) \colon L^2(M,E) \to L^2(M,E)$ is compact.
\end{proposition}
\todo[inline]{say something about the case of an open manifold?}
\todo[inline]{say something about the case of an open manifold!}
% section analysis_of_elliptic_differential_operators (end)
\ No newline at end of file
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