  Consider a differentiable convex function $f: \mathbb{R}^n \supset
\mathrm{dom} f \rightarrow \mathbb{R}.$ The induced spectral function $F$ is
given by $F=f \circ \lambda,$ where $\lambda: \mathbf{M}_n^{sa} \rightarrow
\mathbb{R}^{n}$ is the eigenvalue map. Let us denote by $D_f$ and $D_F$ the
Bregman distances associated with $f$ and $F,$ respectively. In the paper
"Joint and separate convexity of the Bregman distance" written by H. Bauschke
and J. Borwein the following open problem has been suggested. "Is $D_f$ jointly
convex if and only if $D_F$ is?" In this short note we provide a negative
answer to this question.
