  Here we report the first angle-resolved photoemission measurement on nearly
optimally-doped multi-layer Tl-based superconducting cuprates (Tl-2212 and
Tl-1223) and a comparison study to single layer (Tl-2201) compound. A "kink" in
the band dispersion is found in all three compounds but exhibits different
momentum dependence for the single layer and multi-layer compounds, reminiscent
to that of Bi-based cuprates. This layer number dependent renormalization
effect strongly implies that the spin resonance mode is unlikely responsible
for the dramatic renormalization effect near the antinodal region.
