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Unicellularity of the multiplication operator on Banach spaces of formal power series. (English) Zbl 0995.47020

Let \(\ell^p(\beta)\) be the weighted space of sequences defined for a weight \(\beta=(\beta_n)\). The paper gives a sufficient condition for unicellularity of the shift operator in \(\ell^p(\beta)\) in terms of some estimations of the sequence \(\beta\).

MSC:

47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
47A25 Spectral sets of linear operators
47A15 Invariant subspaces of linear operators
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