Related papers: Characteristic function of a power partial isometr…
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 show that the constrained characteristic function is a complete unitary invariant for J-constrained completely non-coisometric (c.n.c.) row contractions, where J is a WOT-closed two-sided ideal of the noncommutative analytic Toeplitz…
Using the Sz.-Nagy--Foias theory of contractions, we obtain general results about reducibility for a class of completely nonunitary contractions. These are applied to certain truncated Toeplitz operators, previously considered by…
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 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…
We develop a Sz.-Nagy--Foias-type functional model for a commutative contractive operator tuple $\underline{T} = (T_1, \dots, T_d)$ having $T = T_1 \cdots T_d$ equal to a completely nonunitary contraction. We identify additional invariants…
Based on a careful analysis of functional models for contractive multi-analytic operators we establish a one-to-one correspondence between unitary equivalence classes of minimal contractive liftings of a row contraction and injective…
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…
We introduce characteristic functions for certain contractive liftings of row contractions. These are multi-analytic operators which classify the liftings up to unitary equivalence and provide a kind of functional model. The most important…
The paper presents a new functional model for completely non-unitary contractions on a Hilbert space. This model is based on the observation that the theory of contractions shares a common geometric basis with the extension theory of…
A bounded linear operator $T$ on a Hilbert space is said to be homogeneous if $\varphi(T)$ is unitarily equivalent to $T$ for all $\varphi$ in the group M\"{o}b of bi-holomorphic automorphisms of the unit disc. A projective unitary…
A tuple of commuting Hilbert space operators $(S_1, \dots, S_{n-1}, P)$ having the closed symmetrized polydisc \[ \Gamma_n = \left\{ \left(\sum_{i=1}^{n}z_i, \sum\limits_{1\leq i<j\leq n} z_iz_j, \cdots, \prod_{i=1}^{n}z_i\right) :…
The goal of the present paper is to push Sz.-Nagy--Foias model theory for a completely nonunitary Hilbert-space contraction operator $T$, to the case of a commuting pair of contraction operators $(T_1, T_2)$ having product $T = T_1 T_2$…
The characteristic function of row contractions and liftings of row contractions are complete invariants up to unitary equivalence for row contractions and liftings of row contractions, respectively. We provide alternate proofs for these…
Isometries played a pivotal role in the development of operator theory, in particular with the theory of contractions and polar decompositions and has been widely studied due to its fundamental importance in the theory of stochastic…
We review how some multianalytic inner functions of the Beurling type theorem are associated to row contractions following works of G.Popescu. Motivated by a result on weak Markov dilations, we define a notion of characteristic function for…
The characteristic function for a contraction is a classical complete unitary invariant devised by Sz.-Nagy and Foias. Just as a contraction is related to the Szego kernel $k_S(z,w) = (1 - z\ow)^{-1}$ for $|z|, |w| < 1$, by means of…
This article develops several functional models for a given $\Gamma_n$-contraction. The first model is motivated by the Douglas functional model for a contraction. We then establish factorization results that clarify the relationship…
A characteristic function is a special operator-valued analytic function defined on the open unit ball of $\mathbb{C}^n$ associated with an $n$-tuple of commuting row contraction on some Hilbert space. In this paper, we continue our study…
To each finite-dimensional operator space $E$ is associated a commutative operator algebra $UC(E)$, so that $E$ embeds completely isometrically in $UC(E)$ and any completely contractive map from $E$ to bounded operators on Hilbert space…