Local spectral properties of typical contractions on \(\ell_p,\)-$\,$spaces

Abstract

We study some local spectral properties of contraction operators on $\ell_p$, $1<p<\infty$ from a Baire category point of view, with respect to the Strong$^*$ Operator Topology. In particular, we show that a typical contraction on $\ell_p$ has Dunford's Property (C) 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 $\ell_p$.