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 \(\beta\).


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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