\begin{equation} \begin{split} \min_{X} \, \frac{1}{2}\|X-Y\|_{\text{Fro}}^{2}+\lambda\|X\|_{*} \end{split} \end{equation}
where $X, Y \in \mathbb{C}^{n \times n}$ and $Y$ is given. $\|\cdot\|_{*}$ denotes the nuclear norm. What's the solution?
If the matrices are real, the problem has an analytic solution known as the spectral soft-thresholding operator. But I don't know what the solution is when the matrices are complex. Do the solutions have the same form?