Related papers: $\lambda$-Toeplitz operators with analytic symbols
Using the approach based on sesquilinear forms, we introduce Toeplitz operator in the analytic Bergman space on the upper half-plane with strongly singular symbols, derivatives of measures. Conditions for boundedness and compactness of such…
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…
In this paper we study the Bergman-Toeplitz operator $T_{\psi}$ induced by $\psi(w) = K_{\Omega}^{-\alpha}(w,w)d_{\Omega}^{\beta}(w)$ with $\alpha, \beta \geq 0$ acting from a weighted $L^p$-space $L_a^p(\Omega)$ to another one…
For a bounded linear operator $T$ acting on a reproducing kernel Hilbert space $\mathcal{H}(\Omega)$ over some non-empty set $\Omega$, the Berezin range and the Berezin radius of $T$ are defined respectively, by $\text{Ber}(T) := \{\langle…
In this paper, we characterize operator-theoretic properties (boundedness, compactness, and Schatten class membership) of Toeplitz operators with positive measure symbols on weighted Fock-Sobolev spaces of fractional order.
In this paper we characterize when the product of two block Toeplitz operators is a compact perturbation of a block Toeplitz operator on the Hardy space of the open unit disk. Necessary and sufficient conditions are given for the commutator…
We compute the Dixmier trace of pseudo-Toeplitz operators on the Fock space. As an application we find a formula for the Dixmier trace of the product of commutators of Toeplitz operators on the Hardy and weighted Bergman spaces on the unit…
In this paper we investigate the numerical ranges of composition operators whose symbols are elliptic automorphisms of finite orders, on the Hilbert Hardy space $H^2(D)$.
A $7$-tuple of commuting bounded operators $\textbf{T} = (T_1, \dots, T_7)$ on a Hilbert space $\mathcal{H}$ is called a \textit{$\Gamma_{E(3; 3; 1, 1, 1)} $-contraction} if $\Gamma_{E(3; 3; 1, 1, 1)}$ is a spectral set for $\textbf{T}. $…
A classical result by R. Rochberg says that every bounded Toeplitz operator $T$ on the Hilbert Paley-Wiener space $\mathrm{PW}_a^2$ admits a bounded symbol $\varphi$. We generalize this result to Toeplitz operators on the Banach…
We observe that local embedding problems for certain Hardy and Bergman spaces of Dirichlet series are equivalent to boundedness of a class of composition operators. Following this, we perform a careful study of such composition operators…
We investigate the Hardy space $H^1_L$ associated with a self-adjoint operator $L$ defined in a general setting in [S. Hofmann, et. al., Hardy spaces associated to non-negative self-adjoint operators satisfying Davies-Gaffney estimates,…
We study Toeplitz operators with separately radial and radial symbols on the weighted Bergman spaces on the unit ball. The unitary equivalence of such operators with multiplication operators on $\ell^2$ spaces was previously obtained by…
By H\"ormander's $L^2$-m\'ethode, we study some operators in the Hilbert space of weight $L^2(\mathbb{C}, \mathrm{e}^{-|z|^2})$. We prove in each case of operator the existence of its inverse which is also a bounded operator.
We consider the Hilbert-type operator defined by $$ H_{\omega}(f)(z)=\int_0^1 f(t)\left(\frac{1}{z}\int_0^z B^{\omega}_t(u)\,du\right)\,\omega(t)dt,$$ where $\{B^{\omega}_\zeta\}_{\zeta\in\mathbb{D}}$ are the reproducing kernels of the…
Fix a metric space $M$ and let $\mathrm{Lip}_0(M)$ be the Banach space of complex-valued Lipschitz functions defined on $M$. A weighted composition operator on $\mathrm{Lip}_0(M)$ is an operator of the kind $wC_f : g \mapsto w \cdot g \circ…
The aim of this paper is to study when two composition operators on the Hilbert space of Dirichlet series with square summable coefficients belong to the same component or when their difference is compact. As a corollary we show that if a…
In this note, we completely characterize complex symmetric weighted composition differentiation operator on the Hardy space $H^2$ with respect to the conjugation operator $C_{\lambda,\alpha}$. Meanwhile, the normal and self-adjoint of the…
In this paper, we characterize the boundedness and the compactness of weighted composition operators acting on a de Branges-Rovnyak space $\mathcal H(b)$, where the symbol $b$ is a rational function in the unit ball of $H^\infty$ that is…
This paper investigates the essential norm of Toeplitz operators $\mathcal{T}_\mu$ acting from the Bergman space $A_\omega^p$ to $A_\omega^q$ ($1 < p \leq q < \infty$) on the unit ball, where $\mu$ is a positive Borel measure and $\omega…