We have measured the first state-resolved, absolute cross sections for posi
tron excitation of electronic states of an atom or molecule using a high re
solution (DeltaE similar to 25 meV FWHM) beam of positrons from a Penning-M
almberg trap. We present cross sections for the excitation of the low-lying
levels of Ar, H-2, and N-2 for incident positron energies between threshol
d and 30 eV. For Ar and H-2, comparison can be made with theoretical calcul
ations, and, in the case of H-2, the results resolve a significant discrepa
ncy between the only two available calculations.