Related papers: A Sufficient condition for compactness of Hankel o…

In this paper, we investigate the boundedness of Toeplitz product $T_{f}T_{g}$ and Hankel product $H_{f}^{*} H_{g}$ on Fock-Sobolev space for two polynomials $f$ and $g$ in $z,\overline{z}\in\mathbb{C}^{n}$. As a result, the boundedness of…

For Toeplitz operators $T_f^{(t)}$ acting on the weighted Fock space $H_t^2$, we consider the semi-commutator $T_f^{(t)}T_g^{(t)}-T_{fg}^{(t)}$, where $t>0$ is a certain weight parameter that may be interpreted as Planck's constant $\hbar$…

In this article, we study Sobolev homeomorphisms and composition operators on homogeneous Lie groups. We prove that a measurable homeomorphism $\varphi: \Omega \to\widetilde{\Omega}$ belongs to the Sobolev space $L^{1}_{q}(\Omega;…

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…

In 1987, Shapiro shew that composition operator induced by symbol $\phi$ is compact on the Lipschltz space if and only if the infinity norm of $\phi$ is less than 1 by a spectral-theoretic argument, where $\phi$ is a holomorphic self-map of…

We derive a necessary condition for compactness of the weighted $\overline\partial$-Neumann operator on the space $L^2(\mathbb C^n,e^{-\varphi})$, under the assumption that the corresponding weighted Bergman space of entire functions has…

Our study is focused on the dynamics of weighted composition operators defined on a locally convex space $E\hookrightarrow (C(X),\tau_p)$ with $X$ being a topological Hausdorff space containing at least two different points and such that…

Let $\varphi:\mathbb{D} \to \mathbb{D}$ be a holomorphic map with a fixed point $\alpha\in\mathbb{D}$ such that $0\leq |\varphi'(\alpha)|<1$. We show that the spectrum of the composition operator $C_\varphi$ on the Fr\'echet space $…

We give estimates for the approximation numbers of composition operators on $H^2$, in terms of some modulus of continuity. For symbols whose image is contained in a polygon, we get that these approximation numbers are dominated by $\e^{- c…

We consider Toeplitz and Hankel operators with piecewise continuous generating functions on $l^p$-spaces and the Banach algebra generated by them. The goal of this paper is to provide a transparent symbol calculus for the Fredholm property…

We study composition operators on spaces of holomorphic Lipschitz functions defined on the open unit ball of a complex Banach space. Our approach is based on the linearization of the symbol through the holomorphic Lipschitz-free spaces,…

In this paper, we study hyponormal weighed composition operators on the Hardy and weighted Bergman spaces. For functions $\psi \in A(\mathbb{D})$ which are not the zero function, we characterize all hyponormal compact weighted composition…

Let $\Omega\subseteq\mathbb C^n$ be a bounded symmetric domain and $f :\Omega \to \Omega^\prime\subseteq \mathbb C^n$ be a proper holomorphic mapping which is factored by a finite complex reflection group $G.$ We identify a family of…

When G is a region in the complex plane, compact composition operators on the uniform algebra of bounded analytic functions on G and the spectra of these operators were described by D. Swanton, Compact composition operators on B(D), Proc.…

The geometric descriptions of the (essential) spectra of Toeplitz operators with piecewise continuous symbols are among the most beautiful results about Toeplitz operators on Hardy spaces $H^p$ with $1<p<\infty$. In the Hardy space $H^1$,…

We obtain a complete characterization of the bounded Hausdorff operators acting on a Fock space $F^p_\alpha$ and taking its values into a larger one $F^q_\alpha,\ 0 < p \leq q \leq \infty,$ as well as some necessary or sufficient conditions…

For weighted Toeplitz operators $\T^N_\phi$ defined on spaces of holomorphic functions in the unit ball, we derive regularity properties of the solutions $f$ to the integral equation $\T^N_\phi(f)=h$ in terms of the regularity of the symbol…

We consider Toeplitz operators with bounded symbol acting on the Bergman space of the unit disk and assess their hyponormality. We will mainly be concerned with the symbol $\varphi(z)=z^{n}|z|^{2s}+a(t)\bar{z}^{m}|z|^{2t}$, where $s$ and…

Using the model theory for Toeplitz operators with smooth symbols developed by the fourth author in the 80's, we study whether such operators $T_{F}$ can be embedded into a $C_{0}$-semigroup of operators on the Hardy space $H^p$ of the open…

The notion of slant H-Toeplitz operator $V_\phi$ on the Hardy space $H^2$ is introduced and its characterizations are obtained. We have shown that an operator on the space $H^2$ is slant H-Toeplitz if and only if its matrix is a slant…