Related papers: Schur product with operator-valued entries

In this article we consider the generalized integral operators acting on the Hilbert space $H^2$. We characterize when these operators are uniform, strong and weakly asymptotic Toeplitz and Hankel operators. Moreover we completely describe…

We study in this paper properties of Schur multipliers of Schatten von Neumann classes $\boldsymbol{S}_p$. We prove that for $p\le1$, Schur multipliers of $\boldsymbol{S}_p$ are necessarily completely bounded. We also introduce for $p\le1$…

Let $\mathcal{B}(\mathcal{H})$ denote the Banach algebra of all bounded linear operators acting on complex Hilbert spaces $\mathcal{H}$. In this paper, we first establish several sharply refined versions of Bohr's inequality analogues with…

In this paper we use orthonormal basis for the Hardy space $H^{2}(\mathbb{T})$, formed by rational functions, to characterize complex symmetric Toeplitz operators on $H^{2}(\mathbb{T})$. As a result, we get examples of these operators whose…

We introduce and give a more or less complete study of a family of branching-Toeplitz operators on the Hilbert space $\ell^2(T_q)$ indexed by a rooted homogeneous tree $T_q$ of degree $q\ge 2$. The finite dimensional analogues of such…

We establish connections between Schur parameters of the Schur class operator-valued functions, the corresponding simple conservative realizations, lower triangular Toeplitz matrices, and Kre\u\i n shorted operators. By means of Schur…

For Toeplitz operators on bounded symmetric domains of arbitrary rank, we define a Hilbert quotient module corresponding to partitions of length $1$ and prove that it belongs to the Macaev class ${\mathcal{L}}^{n,\infty}$. We next obtain an…

In this article we study the action of the the Hilbert matrix operator $\mathcal H$ from the space of bounded analytic functions into conformally invariant Banach spaces. In particular, we describe the norm of $\mathcal{H}$ from $H^\infty$…

We extend to multilinear Hankel operators the fact that some truncations of bounded Hankel operators are bounded. We prove and use a continuity property of bilinear Hilbert transforms on products of Lipschitz spaces and Hardy spaces.

The boundedness and compactness of Toeplitz operator from $A_\omega^p$ to $A_\omega^q$ with doubling weights $\omega$ are studied in this paper. The characterizations of Schatten class Toeplitz operators and Volterra operators on…

We give one sufficient and two necessary conditions for boundedness between Lebesgue or Lorentz spaces of several classes of bilinear multiplier operators closely connected with the bilinear Hilbert transform.

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…

In this note we describe centralizers of Toeplitz operators with polynomial symbols on the Bergman space. As a consequence it is shown that if an element of the norm closed algebra generated by all Toeplitz operators commutes with a…

In this article we introduce several new examples of Wiener pairs $\mathcal{A} \subseteq \mathcal{B}$, where $\mathcal{B} = \mathcal{B}(\ell^2(X;\mathcal{H}))$ is the Banach algebra of bounded operators acting on the Hilbert space-valued…

We construct explicit examples of non-trivial nilpotent Toeplitz operators on Bergman spaces of certain Reinhardt domains in $\mathbb{C}^2$.

By establishing some reproducing kernel estimates, we characterize the bounded, compact and Schatten $p$-class Toeplitz operators with positive measure symbols on the weighted Fock space $F^2_{\alpha,w}$ for $p\geq1$, where $w$ is a weight…

In this paper, we generalize the notion of joint eigenvalues and joint spectrum of matrices and operator tupples on a bi complex Hilbert space. We observe that unlike the spectrum of a bounded operator on a bi complex Hilbert space is…

We initiate a study of asymptotic Toeplitz operators on the Hardy space $H^2(\mathbb{D}^n)$ (over the unit polydisc $\mathbb{D}^n$ in $\mathbb{C}^n$). We also study the Toeplitz operators in the polydisc setting. Our main results on…

This paper is a sequel to [6]. In that paper we transferred the discussions in [1] and [13] concerning almost invariant half-spaces for operators on complex Banach spaces to the context of operators on Hilbert space, and we gave easier…

We provide sufficient and necessary conditions guaranteeing equations $(A+B)^*=A^*+B^*$ and $(AB)^*=B^*A^*$ concerning densely defined unbounded operators $A,B$ between Hilbert spaces. We also improve the perturbation theory of selfadjoint…