Related papers: Toeplitz Operators in Hilbert Space over Graphs

We define positive Toeplitz operators between harmonic Bergman-Besov spaces $b^p_\alpha$ on the unit ball of $\mathbb{R}^n$ for the full ranges of parameters $0<p<\infty$, $\alpha\in\mathbb{R}$. We give characterizations of bounded and…

We study self-similar groupoid actions on arbitrary directed graphs together with $\mathbb{T}$-valued twists that exhaust the second cohomology group of the associated Zappa-Sz\'ep product category. We define and analyse the associated…

The maximal algebras of scalar Toeplitz matrices are known to be formed by generalized circulants. The identification of algebras consisting of block Toeplitz matrices is a harder problem, that has received little attention up to now. We…

In this paper we study mapping properties of Toeplitz-like operators on weighted Bergman spaces of bounded strongly pseudconvex domains in $\mathbb{C}^n$. In particular we prove that a Toeplitz operator built using as kernel a weighted…

This paper studies the \(k^{th}-\)order slant Toeplitz and slant little Hankel operators on the weighted Bergman space \(\mathcal{A}_\alpha^2(\mathbb{D})\). These operators are constructed using a slant shift operator \(W_k\) composed with…

This paper mainly studies totally Abelian operators in the context of analytic Toeplitz operators on both the Hardy and Bergman space. When the symbol is a meromorphic function on $\mathbb{C}$, we establish the connection between totally…

We prove a spatial Isomorphism between two spaces of matrix valued truncated Toeplitz operators.

This tutorial paper presents a survey of results, both classical and new, linking inner functions and operator theory. Topics discussed include invariant subspaces, universal operators, Hankel and Toeplitz operators, model spaces, truncated…

Motivated by the canonical decomposition of contractions on Hilbert spaces, we investigate when contractive Toeplitz operators on vector-valued Hardy spaces on the unit disc admit a non-zero reducing subspace on which its restriction is…

We address the question of describing the membership to Schatten-Von Neumann ideals $\mathcal{S}_ p$ of integration operators $(T_ g f)(z)=\int_{0}^{z}f(\zeta)\,g'(\zeta)\,d\zeta$ acting on Dirichlet type spaces. We also study this problem…

Let us consider, for $n \geq 3$, the Cartan domain $\mathrm{D}_n^{\mathrm{IV}}$ of type IV. On the weighted Bergman spaces $\mathcal{A}^2_\lambda(\mathrm{D}_n^{\mathrm{IV}})$ we study the problem of the existence of commutative…

In this paper we are concerned with hyponormality and subnormality of block Toeplitz operators acting on the vector-valued Hardy space $H^2_{\mathbb{C}^n}$ of the unit circle. Firstly, we establish a tractable and explicit criterion on the…

We study the Hopf structure of a class of dual operator algebras corresponding to certain semigroups. This class of algebras arises in dilation theory, and includes the noncommutative analytic Toeplitz algebra and the multiplier algebra of…

A truncated Toeplitz operator is the compression $A_{\phi}:\K_{\Theta} \to \K_{\Theta}$ of a Toeplitz operator $T_{\phi}:H^2\to H^2$ to a model space $\K_{\Theta} := H^2 \ominus \Theta H^2$. For $\Theta$ inner, let $\T_{\Theta}$ denote the…

Truncated Toeplitz operators and their asymmetric versions are studied in the context of the Hardy space $H^p$ of the half-plane for $1<p<\infty$. It is shown that they are equivalent after extension to $2 \times 2$ matricial Toeplitz…

Toeplitz operators are fundamental and ubiquitous in signal processing and information theory as models for linear, time-invariant (LTI) systems. Due to the fact that any practical system can access only signals of finite duration,…

Let $D$ be an irreducible bounded symmetric domain with biholomorphism group $G$ with maximal compact subgroup $K$. For the Toeplitz operators with $K$-invariant symbols we provide explicit simultaneous diagonalization formulas on every…

In this paper, we obtain some $L^{p}$ mapping properties of the Bergman-Toeplitz operator \[ f\longrightarrow T_{K^{-\alpha}}\left(f\right):=\intop_{\Omega}K_{\Omega}\left(\cdot,w\right)K^{-\alpha}\left(w,w\right)f\left(w\right)dV(w) \] on…

Truncated Toeplitz operators in a model space are C--symmetric with respect to a natural conjugation in that space. We show that this and another conjugation associated to an orthogonal decomposition possess unique properties and we study…

In this paper we consider a class of unbounded Toeplitz operators with rational matrix symbols that have poles on the unit circle and employ state space realization techniques from linear systems theory, as used in our earlier analysis in…