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Absolute transition frequencies of the $2s\; ^2{\rm S}_{1/2} \rightarrow2p\;^2\mathrm{P}_{1/2,3/2}$ transitions in Be$^+$ were measured for theisotopes $^{7,9-12}$Be. The fine structure splitting of the $2p$ state and itsisotope dependence are extracted and compared to results of \textit{ab initio}calculations using explicitly correlated basis functions, includingrelativistic 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 andexperiment by 2 orders of magnitude, and good agreement is observed. Thisrepresents one of the most accurate tests of quantum electrodynamics formany-electron systems, being insensitive to nuclear uncertainties.

Precision Test of Many-Body QED in the Be$^+$ $2p$ Fine Structure Doublet Using Short-Lived Isotopes