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Extensions of symmetric operators I: The inner characteristic function case

R.T.W. Martin (2015)

Concrete Operators

Given a symmetric linear transformation on a Hilbert space, a natural problem to consider is the characterization of its set of symmetric extensions. This problem is equivalent to the study of the partial isometric extensions of a fixed partial isometry. We provide a new function theoretic characterization of the set of all self-adjoint extensions of any symmetric linear transformation B with finite equal indices and inner Livšic characteristic function θB by constructing a bijection between the...

Functional models and asymptotically orthonormal sequences

Isabelle Chalendar, Emmanuel Fricain, Dan Timotin (2003)

Annales de l’institut Fourier

Suppose H 2 is the Hardy space of the unit disc in the complex plane, while Θ is an inner function. We give conditions for a sequence of normalized reproducing kernels in the model space K Θ = H 2 ⊖ Θ H 2 to be asymptotically close to an orthonormal sequence. The completeness problem is also investigated.

Generalized eigenfunction expansions and spectral decompositions

Mihai Putinar (1997)

Banach Center Publications

The paper relates several generalized eigenfunction expansions to classical spectral decomposition properties. From this perspective one explains some recent results concerning the classes of decomposable and generalized scalar operators. In particular a universal dilation theory and two different functional models for related classes of operators are presented.

Non-hyperreflexive reflexive spaces of operators

Roman V. Bessonov, Janko Bračič, Michal Zajac (2011)

Studia Mathematica

We study operators whose commutant is reflexive but not hyperreflexive. We construct a C₀ contraction and a Jordan block operator S B associated with a Blaschke product B which have the above mentioned property. A sufficient condition for hyperreflexivity of S B is given. Some other results related to hyperreflexivity of spaces of operators that could be interesting in themselves are proved.

On a decomposition for pairs of commuting contractions

Zbigniew Burdak (2007)

Studia Mathematica

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

Yoichi Uetake (1997)

Annales Polonici Mathematici

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 C 0 · multi-contractions having a regular dilation

Dan Popovici (2005)

Studia Mathematica

Commuting multi-contractions of class C 0 · and having a regular isometric dilation are studied. We prove that a polydisc contraction of class C 0 · 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

Zolotarev, Vladimir A., Hatamleh, Raéd (2006)

Serdica Mathematical Journal

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.

Currently displaying 21 – 40 of 106