The cross sections for the pp -> ppK+K- reaction were measured at three beam energies 2.65, 2.70, and 2.83 GeV at the COSY-ANKE facility. The shape of the K+K- spectrum at low invariant masses largely reflects the importance of Kbar{K} final state interactions. It is shown that these data can be understood in terms of an elastic K+K- rescattering plus a contribution coming from the production of a K0bar{K}0 pair followed by a charge-exchange rescattering. Though the data are not yet sufficient to establish the size of the cusp at the K0bar{K}0 threshold, the low mass behaviour suggests that isospin-zero production is dominant.
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