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Weighted shift operators on \(\ell _ p\) spaces. (English) Zbl 0615.47023

The analytic-spectral structure of the commutant of a weighted shift operator defined on a \(\ell_ p\) space \((1\leq p<\infty)\) is studied. The cases unilateral, bilateral and quasinilpotent are treated. We apply the results to study certain questions related to unicellularity, strictly cyclicity and the existence of hyperinvariant subspaces.

MSC:

47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
47A15 Invariant subspaces of linear operators
46A45 Sequence spaces (including Köthe sequence spaces)
47A65 Structure theory of linear operators
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