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arXiv · 2105.04635

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

Sophie Grivaux·Étienne Matheron
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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 $\ell_p$.

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Sophie Grivaux, Étienne Matheron. 2021-05-10. Local spectral properties of typical contractions on \(\ell_p,\)-$\,$spaces. https://arxiv.org/abs/2105.04635

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