Related papers: Compactness of Hankel operators with continuous sy…

Let $\mathscr{H}^2$ denote the Hilbert space of Dirichlet series with square-summable coefficients. We study composition operators $\mathscr{C}_\varphi$ on $\mathscr{H}^2$ which are generated by symbols of the form $\varphi(s) = c_0s +…

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.…

We investigate the compactness of composition operators on the Hardy space of Dirichlet series induced by a map $\varphi(s)=c_0s+\varphi_0(s)$, where $\varphi_0$ is a Dirichlet polynomial. Our results depend heavily on the characteristic…

Let $\phi$ be an analytic map taking the unit disk $\mathbb{D}$ into itself. We establish that the class of composition operators $f \mapsto C_\phi(f) = f \circ \phi$ exhibits a rather strong rigidity of non-compact behaviour on the Hardy…

Let $\lambda_i (i=1,...,k)$ be any nonzero complex scalars and $\varphi_i (i=1,..,k)$ be any analytic self-maps of the unit disk $\mathbb{D}$. We show that the operator $\sum_{i=1}^k\lambda_iC_{\varphi_i}$ is compact on the Bloch space…

We show that every non-compact weighted composition operator $f \mapsto u\cdot (f\circ\phi)$ acting on a Hardy space $H^p$ for $1 \leq p < \infty$ fixes an isomorphic copy of the sequence space $\ell^p$ and therefore fails to be strictly…

In this paper, we study the boundedness and the compactness of the little Hankel operators $h_b$ with operator-valued symbols $b$ between different weighted vector-valued Bergman spaces on the open unit ball $\mathbb{B}_n$ in…

We give a necessary and sufficient condition for a holomorphic self-map $\phi$ of the tridisc to induce a bounded composition operator on the associated Hardy space. This condition depends on the behaviour of the first and the second…

In this paper, we introduce the metric operator for a compact homogeneous Finsler space, and use it to investigate the geodesic orbit property. We define the notion of standard homogeneous $(\alpha_1,\cdots,\alpha_s)$-metric which…

Motivated by the Sarason problem on the products of Hankel and Toeplitz operators on analytic function spaces, we characterize the compactness of products of block Hankel and Toeplitz operators on the vector-valued Hardy space of the unit…

By means of hypercyclic operator theory, we complement our previous results on hypercyclic holomorphic maps between complex Euclidean spaces having slow growth rates,by showing {\it abstract abundance} rather than {\it explicit existence}.…

We show there is a solution operator to $\bar{\partial}$ which is bounded as a map $W^{s}_{(0,1)}(\Omega)\cap\mbox{ker }\bar{\partial}\rightarrow W^{s}(\Omega)$ for all $s\ge 0$.

We extend a classical result of Caughran/Schwartz and another recent result of Gunatillake by showing that if D is a bounded, convex domain in n-dimensional complex space, m is a holomorphic function on D and bounded away from zero toward…

Let $h$ be a harmonic function defined on a spherical disk. It is shown that $\Delta^k |h|^2$ is nonnegative for all $k\in \mathbb{N}$ where $\Delta$ is the Laplace-Beltrami operator. This fact is generalized to harmonic functions defined…

Let $n \geq 4$ and let $\Omega$ be a bounded hyperconvex domain in $\mathbb{C}^{n}$. Let $\varphi$ be a negative exhaustive smooth plurisubharmonic function on $\Omega$. We show that any holomorphic function defined on a connected open…

For $0<p\leq\infty$, let $F^{p}_\varphi$ be the Fock space induced by a weight function $\varphi$ satisfying $ dd^c \varphi \simeq \omega_0$. In this paper, given $p\in (0, 1]$ we introduce the concept of weakly localized operators on $…

Recently it was proven that for a convex subset of $\mathbb{R}^{n}$ that has infinitely many extreme vectors, the Nehari theorem fails, that is, there exists a bounded Hankel operator $\Ha_{\phi}$ on the Paley--Wiener space $\PW(\Omega)$…

We describe all isometries of the $q$-numerical radius on the space ${\mathcal K}(\mathcal H)$ of compact operators on a (possibly infinite-dimensional) Hilbert space $\mathcal H$.

Let $X$ be a ball Banach function space on ${\mathbb R}^n$. Let $\Omega$ be a Lipschitz function on the unit sphere of ${\mathbb R}^n$,which is homogeneous of degree zero and has mean value zero, and let $T_\Omega$ be the convolutional…

In this paper, we consider the following problem involving fractional Laplacian operator: \begin{equation}\label{eq:0.1} (-\Delta)^{\alpha} u= |u|^{2^*_\alpha-2-\varepsilon}u + \lambda u\,\, {\rm in}\,\, \Omega,\quad u=0 \,\, {\rm on}\, \,…