  Let $\mathcal H$ and $\mathcal K$ be real Hilbert spaces and $T \in
\mathcal{B} (\mathcal H,\mathcal K)$ an injective operator with closed range
and Moore-Penrose inverse $T^\dagger$. Based on the well-known characterization
of proximity operators by Moreau, we prove that for any proximity operator
$\text{Prox} \colon \mathcal K \to \mathcal K$ the operator $T^\dagger \,
\text{Prox} \, T$ is a proximity operator on the linear space $\mathcal H$
equipped with a suitable norm. In particular, it follows for the frequently
applied soft shrinkage operator $\text{Prox} = S_{\lambda}\colon \ell_2
\rightarrow \ell_2$ and any frame analysis operator $T\colon \mathcal H \to
\ell_2$, that the frame shrinkage operator $T^\dagger\, S_\lambda\, T$ is a
proximity operator in a suitable Hilbert space.
