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${}^{\ast }$ 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 ${\ell }_p$.

arXiv comment19 p

References in corpus (1)

• Linear dynamical systems on Hilbert spaces: typical properties and explicit examples