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

Yousefi, B.

Stud. Math. 147, No. 3, 201-209 (2001).

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 \(\beta\).

Reviewer: Vladimir V.Kisil (Leeds)

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

Keywords:

invariant subspace lattice; Banach space of formal power series; cyclic vector; unicellular operator; shift operator; weighted \(\ell^p\) space