Schur-class Multipliers on the Fock Space: De Branges-rovnyak Reproducing Kernel Spaces and Transfer-function Realizations
نویسنده
چکیده
We introduce and study a Fock-space noncommutative analogue of reproducing kernel Hilbert spaces of de Branges-Rovnyak type. Results include: use of the de Branges-Rovnyak space H(KS) as the state space for the unique (up to unitary equivalence) observable, coisometric transfer-function realization of the Schur-class multiplier S, realization-theoretic characterization of inner Schur-class multipliers, and a calculus for obtaining a realization for an inner multiplier with prescribed left zero-structure. In contrast with the parallel theory for the Arveson space on the unit ball B ⊂ C (which can be viewed as the symmetrized version of the Fock space used here), the results here are much more in line with the classical univariate case, with the extra ingredient of the existence of all results having both a “left” and a “right” version. Dedicated to the memory of Tiberiu Constantinescu
منابع مشابه
Schur-class Multipliers on the Arveson Space: De Branges-rovnyak Reproducing Kernel Spaces and Commutative Transfer-function Realizations
An interesting and recently much studied generalization of the classical Schur class is the class of contractive operator-valued multipliers S(λ) for the reproducing kernel Hilbert space H(kd) on the unit ball B d ⊂ C, where kd is the positive kernel kd(λ,ζ) = 1/(1 − 〈λ, ζ〉) on B . The reproducing kernel space H(KS) associated with the positive kernel KS(λ,ζ) = (I −S(λ)S(ζ)∗) · kd(λ,ζ) is a nat...
متن کاملReproducing Kernels, De Branges-rovnyak Spaces, and Norms of Weighted Composition Operators
SPACES, AND NORMS OF WEIGHTED COMPOSITION OPERATORS MICHAEL T. JURY Abstract. We prove that the norm of a weighted composition operator on the Hardy space H2 of the disk is controlled by the norm of the weight function in the de Branges-Rovnyak space associated to the symbol of the composition operator. As a corollary we obtain a new proof of the boundedness of composition operators on H2, and ...
متن کاملDe Branges–Rovnyak Realizations of Operator-Valued Schur Functions on the Complex Right Half-Plane
We give a controllable energy-preserving and an observable co-energypreserving de Branges–Rovnyak functional model realization of an arbitrary given operator Schur function defined on the complex right-half plane. We work the theory out fully in the right-half plane, without using results for the disk case, in order to expose the technical details of continuous-time systems theory. At the end o...
متن کاملA characterization of Schur multipliers between character-automorphic Hardy spaces
We give a new characterization of character-automorphic Hardy spaces of order 2 and of their contractive multipliers in terms of de Branges Rovnyak spaces. Keys tools in our arguments are analytic extension and a factorization result for matrix-valued analytic functions due to Leech.
متن کاملTransfer-function Realization for Multipliers of the Arveson Space
An interesting and recently much studied generalization of the classical Schur class is the class of contractive operator-valued multipliers for the reproducing kernel Hilbert space H(kd) on the unit ball B d ⊂ C, where kd is the positive kernel kd(λ, ζ) = 1/(1−〈λ, ζ〉) on B . We study this space from the point of view of realization theory and functional models of de BrangesRovnyak type. We hig...
متن کامل