相关论文: Beurling quotient subspaces for covariant represen…

Using the Wold-von Neumann decomposition for the isometric covariant representations due to Muhly and Solel, we prove an explicit representation of the commutant of a doubly commuting pure isometric representation of the product system over…

We study completely contractive representations of product systems $X$ of correspondences over the semigroup $\mathbb{Z}_+^k$. We present a necessary and sufficient condition for such a representation to have a regular isometric dilation.…

We obtain a Shimorin-Wold-type decomposition for a doubly commuting covariant representation of a product system of $C^*$-correspondences. This extends a recent Wold-type decomposition by Jeu and Pinto for a $q$-doubly commuting isometries.…

Let $X=(X(n))_{n \in \mathbb{Z_+}}$ be a standard subproduct system of $C^*$-correspondences over a $C^*$-algebra $\mathcal M.$ Assume $T=(T_n)_{n \in \mathbb{Z_+}}$ to be a pure completely contractive, covariant representation of $X$ on a…

Let $H^2(\mathbb{D}^n)$ denote the Hardy space over the polydisc $\mathbb{D}^n$, $n \geq 2$. A closed subspace $\mathcal{Q} \subseteq H^2(\mathbb{D}^n)$ is called Beurling quotient module if there exists an inner function $\theta \in…

We obtain Berger-Coburn-Lebow (BCL)-representation for pure isometric covariant representation of product system over $\mathbb{N}_0^2$. Then the corresponding complete set of (joint) unitary invariants is studied, and the BCL-…

In this paper we propose a new technical tool for analyzing representations of Hilbert $C^*$-product systems. Using this tool, we give a new proof that every doubly commuting representation over $\mathbb{N}^k$ has a regular isometric…

We discuss representations of product systems (of $W^*$-correspondences) over the semigroup $\mathbb{Z}^n_+$ and show that, under certain pureness and Szego positivity conditions, a completely contractive representation can be dilated to an…

We obtain a Halmos-Richter-type wandering subspace theorem for covariant representations of C*-correspondences. Further the notion of Cauchy dual and a version of Shimorin's Wold-type decomposition for covariant representations of…

We prove a Hankel-variant commutant lifting theorem. This also uncovers the complete structure of the Beurling-type reducing and invariant subspaces of Hankel operators. Kernel spaces of Hankel operators play a key role in the analysis.

We show that a Beurling type theory of invariant subspaces of noncommutative $H^2$ spaces holds true in the setting of subdiagonal subalgebras of $\sigma$-finite von Neumann algebras. This extends earlier work of Blecher and Labuschagne for…

We introduce the notion of $k$-regular factorizations for contractions into $k$ factors, generalizing the classical notion of regular factorization due to Sz.-Nagy and Foia\c{s}, and develop a systematic framework for their analysis. Using…

In a previous paper, we presented an Abstract Beurling's Theorem for valuation Hilbert modules over valuation algebras. In this paper, we shall apply this theorem to obtain complete descriptions of the closed invariant subspaces of a number…

Olofsson introduced a growth condition regarding elements of an orbit for an expansive operator and generalized Richter's wandering subspace theorem. Later on, using the Moore-Penrose inverse, Ezzahraoui, Mbekhta, and Zerouali extended the…

The techniques developed by Popescu, Muhly-Solel and Good for the study of algebras generated by weighted shifts are applied to generalize results of Sarkar and of Bhattacharjee-Eschmeier-Keshari-Sarkar concerning dilations and invariant…

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…

We use operator algebras and operator theory to obtain new result concerning Berezin quantization of compact K\"ahler manifolds. Our main tool is the notion of subproduct systems of finite-dimensional Hilbert spaces, which enables all…

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…

We develop a dilation theory for row contractions subject to constraints determined by sets of noncommutative polynomials. Under natural conditions on the constraints, we have uniqueness for the minimal dilation. A characteristic function…

We develop a theory of Valuation Hilbert Modules and prove a version of Beurling's theorem for these. Then we apply our version of Beurling's theorem to obtain complete descriptions of the closed invariant subspaces of a number of Hilbert…