Abstract
We study some local spectral properties of contraction operators on ℓp, 1 < p < ∞ from a Baire category point of view, with respect to the Strong* Operator Topology. In particular, we show that a typical contraction on ℓp has Dunford’s Property (C) but neither Bishop’s Property (β) nor the Decomposition Property (δ), and is completely indecomposable. We also obtain some results regarding the asymptotic behavior of orbits of typical contractions on ℓp.
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To the memory of Jorg Eschmeier
This work was supported in part by the project FRONT of the French National Research Agency (grant ANR-17-CE40-0021) and by the Labex CEMPI (ANR-11-LABX-0007-01).
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Grivaux, S., Matheron, É. Local Spectral Properties of Typical Contractions on ℓp-Spaces. Anal Math 48, 755–778 (2022). https://doi.org/10.1007/s10476-022-0168-0
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DOI: https://doi.org/10.1007/s10476-022-0168-0