The electronic structure of thin Co nanoislands on Cu(111) has been investigated by scanning tunneling spectroscopy at low temperature. Two surface related economic states are found. An energetically localized state in the spectrum at 0.31 eV below the Fermi level (E_F) and a mainly unoccupied dispersive state, giving rise to quantum interference patterns of standing electron waves on the Co surface. Ab initio calculations reveal that both electronic states are spin-polarized, originating from d_3z²−r²-minority and sp-majority bands, respectively.