Related papers: Positive Toeplitz Operators from a Weighted Harmon…

We consider three problems connected with coinvariant subspaces of the backward shift operator in Hardy spaces $H^p$: 1) properties of truncated Toeplitz operators; 2) Carleson-type embedding theorems for the coinvariant subspaces; 3)…

This paper introduces the classically successful theory of Toeplitz operators on the Hardy space over the unit disk to a new domain in $\mathbb C^d$ -- the symmetrized polydisk.

We define co-Toeplitz operators, a new class of Hilbert space operators, in order to define a co-Toeplitz quantization scheme that is dual to the Toeplitz quantization scheme introduced by the author in the setting of symbols that come from…

This is a review paper based on the series of our papers devoted to a structure of true-poly-analytic Bergman function spaces over the upper half-plane in the complex plane and to a detailed study of properties of Toeplitz operators with…

We extend results on compressed Toeplitz operators on the backward shift invariant subspaces of $H^2 $ to the context of the spaces $H^p$, $1<p<\infty.$

Let $\lambda$ be a complex number in the closed unit disc $\overline{\Bbb D}$, and $\cal H$ be a separable Hilbert space with the orthonormal basis, say, ${\cal E}=\{e_n:n=0,1,2,\cdots\}$. A bounded operator $T$ on $\cal H$ is called a…

We consider weighted composition operators on spaces of analytic functions on the unit disc, which take values in some complex Banach space. We provide necessary and sufficient conditions for the boundedness and (weak) compactness of…

In this paper, we characterize invertible Toeplitz products on a number of Banach spaces of analytic functions, including weighted Bergman space $L^p_a (\mathbb{B}_n, dv_\gamma)$, the Hardy space $H^p(\partial \mathbb{D})$, and the weighted…

We study the weighted composition operators between the Lipschitz space and the space of bounded functions on the set of vertices of an infinite tree. We characterized the boundedness, the compactness, and the boundedness from below of…

We consider the weighted Bergman spaces HL^2(B^d,\mu_{\lambda}), where d\mu_\lambda(z)=c_{\lambda}(1-|z|^2)^lambda d\tau, \tau being the hyperbolic volume measure. These spaces are nonzero if and only if \lambda>d. For 0<\lambda\leq d,…

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…

We study the bounded and the compact weighted composition operators from the Bloch space into the weighted Banach spaces of holomorphic functions on bounded homogeneous domains, with particular attention to the unit polydisk. For bounded…

In this paper, we obtain some interesting reproducing kernel estimates and some Carleson properties that play an important role. We completely characterized every case of the bounded and compact Toeplitz operators on the weighted Bergman…

For $1 < p < \infty$ let $\mathcal{T}_p ^\alpha$ be the norm closure of the algebra generated by Toeplitz operators with bounded symbols acting on the standard weighted Fock space $F_\alpha ^p$. In this paper, we will show that an operator…

We study weighted composition operators acting between Fock spaces. The following results are obtained: (1) Criteria for the boundedness and compactness; (2) Characterizations of compact differences and essential norm; (3) Complete…

The aim of this paper is to define Toeplitz operators between K\"othe spaces, especially power series spaces. We determine the conditions for continuity and compactness of these operators. We define the concept of S-tameness of a family of…

Suppose $n\geq 3$ and let $B$ be the open unit ball in $\mathbb{R}^n$. Let $\varphi: B\to B$ be a $C^2$ map whose Jacobian does not change sign, and let $\psi$ be a $C^2$ function on $B$. We characterize bounded weighted composition…

For any given bounded symmetric domain, we prove the existence of commutative $C^*$-algebras generated by Toeplitz operators acting on any weighted Bergman space. The symbols of the Toeplitz operators that generate such algebras are defined…

We study Toeplitz operators on the Bargmann space, with Toeplitz symbols that are exponentials of inhomogeneous quadratic polynomials. It is shown that the boundedness of such operators is implied by the boundedness of the corresponding…

We define and study Toeplitz operators in the space of Herglotz solutions of the Helmholtz equation in $R^d$. As the most traditional definition of Toeplitz operators via Bergman-type projection is not available here, we use an approach…