A domain in $\mathbb{C}^N$ is a bounded symmetric domain if there exists a norm $\|\cdot\|$ on $\mathbb{C}^N$ such that $U=\{z\in \mathbb{C}^N : \|z\|<1\}$ and if the automorphism group of $U$ denoted by Aut$(U)$ acts transitively on $U$. A domain $G$ in $\mathbb{C}^N$ is a Runge domain if for any holomorphic function $f$ on $G$ there is a sequence of polynomials $p_n$ converging to $f$ uniformly on compact subsets of $G$.
If $U$ is a bounded symmetric domain, must $U$ be a Runge domain? The only thing I know about several complex variables is how little I know about several complex variables. I ran into bounded symmetric domains while doing some research, and I'm hoping they share some of the nice properties that the usual Euclidean open unit ball in $\mathbb{C}^N$ has.