We have investigated valence-band properties of Pt(111) surface covered by an Ag layer. Aside from showing significant changes in the d bands and the sp-like Shockley-type surface resonance depending on the thickness of the Ag layer, our spectroscopic data suggest the formation of an Ag-Pt mixture that progressively develops at the interface upon increasing the annealing temperature of the sample. On a 2-ML system, the Shockley resonance band is partially occupied and exhibits a large Rashba spin-orbit splitting that can be described by a first-principles band-structure calculation based on multiple-scattering theory. For the interface alloy, we have used the coherent potential approximation, which is one of the best models among the so-called single-site (local) theory. We observe a shift of the Shockley resonance due to the alloying process at the interface that probably favors the formation of the well-known triangular reconstruction.