Local spectral properties of typical contractions on ${\mathrm{\ell }}_p,$-$$spaces

We study some local spectral properties of contraction operators on ${\mathrm{\ell }}_p$, $1<p<\mathrm{\infty }$ from a Baire category point of view, with respect to the Strong${}^{\ast }$ Operator Topology. In particular, we show that a typical contraction on ${\mathrm{\ell }}_p$ has Dunford’s Property © but neither Bishop’s Property $(\beta )$ nor the Decomposition Property $(\delta )$, and is completely indecomposable. We also obtain some results regarding the asymptotic behavior of orbits of typical contractions on ${\mathrm{\ell }}_p$.