Related papers: Completely non unitary contractions and Analyticit…
The simplest and most natural examples of completely nonunitary contractions on separable complex Hilbert spaces which have polynomial characteristic functions are the nilpotent operators. The main purpose of this paper is to prove the…
By analytic perturbations, we refer to shifts that are finite rank perturbations of the form $M_z + F$, where $M_z$ is the unilateral shift and $F$ is a finite rank operator on the Hardy space over the open unit disc. Here shift refers to…
In this note we study the completely non unitary contractions on separable complex Hilbert spaces which have polynomial characteristic functions. These operators are precisely those which admit a matrix representation of the form T = S & *…
We consider contractive operators $T$ that are trace class perturbations of a unitary operator $U$. We prove that the dimension functions of the absolutely continuous spectrum of $T$, $T^*$ and of $U$ coincide. In particular, if $U$ has a…
Suppose $\mathcal{T}_{+}(E)$ is the tensor algebra of a $W^{*}$-correspondence $E$ and $H^{\infty}(E)$ is the associated Hardy algebra. We investigate the problem of extending completely contractive representations of $\mathcal{T}_{+}(E)$…
A criterion on the similarity of a (bounded, linear) operator $T$ on a (complex, separable) Hilbert space $\mathcal H$ in terms of shift-type invariant subspaces of $T$ to a contraction of class $C_{\cdot 0}$ with finite unequal defects is…
The goal of the present paper is to introduce and study noncommutative Hardy spaces associated with the regular $\Lambda$-polyball, to develop a functional calculus on noncommutative Hardy spaces for the completely non-coisometric (c.n.c.)…
The characteristic function has been an important tool for studying completely non unitary contractions on Hilbert spaces. In this note, we consider completely non-coisometric contractive tuples of commuting operators on a Hilbert space…
In this paper we show that every conjugation $C$ on the Hardy-Hilbert space $H^{2}$ is of type $C=T^{*}C_{1}T$, where $T$ is an unitary operator and $C_{1}f\left(z\right)=\overline{f\left(\overline{z}\right)}$, with $f\in H^{2}$. In the…
We reconsider studies of Toeplitz operators on function spaces (the weighted Bergman space, the generalized derivative Hardy space) and the H-Toeplitz operators on the Bergman space. Past studies have considered the presence or absence of…
We define the Hardy spaces of free noncommutative functions on the noncommutative polydisc and the noncommutative ball and study their basic properties. Our technique combines the general methods of noncommutative function theory and…
Formally symmetric differential operators on weighted Hardy-Hilbert spaces are analyzed, along with adjoint pairs of differential operators. Eigenvalue problems for such operators are rather special, but include many of the classical…
A contraction $T$ on a (complex, separable) Hilbert space is stable, or of class $C_{0\cdot}$, if $T^n\to 0$ in the strong operator topology. It is proved that for a non-stable pure subnormal contraction $T$ there exists a singular inner…
Absolutely continuous commuting row contractions admit a weak-$*$ continuous functional calculus. Building on recent work describing the first and second dual spaces of the closure of the polynomial multipliers on the Drury-Arveson space,…
In this paper we initiate the study of a fundamental yet untapped random model of non-selfadjoint, bounded linear operators acting on a separable complex Hilbert space. We replace the weights $w_n=1$ in the classical unilateral shift $T$,…
In this paper we initiate the study of composition operators on the noncommutative Hardy space $H^2_{\bf ball}$. Several classical results about composition operators (boundedness, norm estimates, spectral properties, compactness,…
In this expository paper we describe the study of certain non-self-adjoint operator algebras, the Hardy algebras, and their representation theory. We view these algebras as algebras of (operator valued) functions on their spaces of…
A realization is a triple, $(A,b,c)$, consisting of a $d-$tuple, $A= (A =_1, \cdots, A_d )$, $d\in \mathbb{N}$, of bounded linear operators on a separable, complex Hilbert space, $\mathcal{H}$, and vectors $b,c \in \mathcal{H}$. Any such…
By a famous result, functions in backward shift invariant subspaces in Hardy spaces are characterized by the fact that they admit a pseudocontinuation a.e. on $\T$. More can be said if the spectrum of the associated inner function has holes…
Let $\mathbb H$ be the finite direct sums of $H^2(\mathbb D)$. In this paper, we give a characterization of the closed subspaces of $\mathbb H$ which are invariant under the shift, thus obtaining a concrete Beurling-type theorem for the…