On a certain class of nonstationary sequences in Hilbert space.
On a class of -contractions: hyperinvariant subspaces and intertwining operators.
On a decomposition for pairs of commuting contractions
A new decomposition of a pair of commuting, but not necessarily doubly commuting contractions is proposed. In the case of power partial isometries a more detailed decomposition is given.
On a property of weak resolvents and its application to a spectral problem
We show that the poles of a resolvent coincide with the poles of its weak resolvent up to their orders, for operators on Hilbert space which have some cyclic properties. Using this, we show that a theorem similar to the Mlak theorem holds under milder conditions, if a given operator and its adjoint have cyclic vectors.
On multi-contractions having a regular dilation
Commuting multi-contractions of class and having a regular isometric dilation are studied. We prove that a polydisc contraction of class is the restriction of a backwards multi-shift to an invariant subspace, extending a particular case of a result by R. E. Curto and F.-H. Vasilescu. A new condition on a commuting multi-operator, which is equivalent to the existence of a regular isometric dilation and improves a recent result of A. Olofsson, is obtained as a consequence.
On Connection between Characterestic Functions and the Caratheodori Class Functions
2000 Mathematics Subject Classification: 47A65, 45S78.Connection of characteristic functions S(z) of nonunitary operator T with the functions of Caratheodori class is established. It was demonstrated that the representing measures from integral representation of the function of Caratheodori's class are defined by restrictions of spectral measures of unitary dilation, of a restricted operator T on the corresponding defect subspaces.
On Dominating Sequences in the Unit Disc.
On Intertwining Operators.
On Polynomials in Several Hilbert Space Operators.
On the Davis-Kahan-Weinberger Solution of the Norm-Preserving Dilation Problem.
On the Jordan model operators
Operator models and Arveson's curvature invariant
Operator positivity and analytic models of commuting tuples of operators
We study analytic models of operators of class with natural positivity assumptions. In particular, we prove that for an m-hypercontraction on a Hilbert space , there exist Hilbert spaces and ⁎ and a partially isometric multiplier θ ∈ ℳ (H²(),A²ₘ(⁎)) such that and , where A²ₘ(⁎) is the ⁎-valued weighted Bergman space and H²() is the -valued Hardy space over the unit disc . We then proceed to study analytic models for doubly commuting n-tuples of operators and investigate their applications...