Wandering subspaces and quasi-wandering subspaces in the Bergman space.
Wandering subspaces and the Beurling type theorem. II.
Weighted shift operators on lp spaces.
The analytic-spectral structure of the commutant of a weighted shift operator defined on a lp space (1 ≤ p < ∞) 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.
Wold-type extension for N-tuples of commuting contractions
Let (T1,…,TN) be an N-tuple of commuting contractions on a separable, complex, infinite-dimensional Hilbert space ℋ. We obtain the existence of a commuting N-tuple (V1,…,VN) of contractions on a superspace K of ℋ such that each extends , j=1,…,N, and the N-tuple (V1,…,VN) has a decomposition similar to the Wold-von Neumann decomposition for coisometries (although the need not be coisometries). As an application, we obtain a new proof of a result of Słociński (see [9])