  Absolute transition frequencies of the $2s\; ^2{\rm S}_{1/2} \rightarrow
2p\;^2\mathrm{P}_{1/2,3/2}$ transitions in Be$^+$ were measured for the
isotopes $^{7,9-12}$Be. The fine structure splitting of the $2p$ state and its
isotope dependence are extracted and compared to results of \textit{ab initio}
calculations using explicitly correlated basis functions, including
relativistic and quantum electrodynamics effects at the order of $m \alpha^6$
and $m \alpha^7 \ln \alpha$. Accuracy has been improved in both the theory and
experiment by 2 orders of magnitude, and good agreement is observed. This
represents one of the most accurate tests of quantum electrodynamics for
many-electron systems, being insensitive to nuclear uncertainties.
