Related papers: On Shapiro's Compactness Criterion for Composition…

We give examples of results on composition operators connected with lens maps. The first two concern the approximation numbers of those operators acting on the usual Hardy space $H^2$. The last ones are connected with Hardy-Orlicz and…

Let $B_{n}$ be the unit ball in the complex vector space $\mathbb{C}^{n}$, and let $\varphi: B_{n}\rightarrow B_{n}$ be a holomorphic mapping. In this paper, we characterize those symbols $\varphi$ such that composition operators…

Let $\mathbb{D}$ denote the unit disk of $\mathbb{C}$ and let $\Lambda^\alpha(\mathbb{D})$ denote the scale of holomorphic Lipschitz spaces extended to all $\alpha\in\mathbb{R}$. For arbitrary $\alpha, \beta\in\mathbb{R}$, we characterize…

In this research article the necessary and sufficient conditions for the norm of composition operator $C_{\Phi}$ on $\mathcal{A}_{\alpha}^2(H)$ to be one are obtained. Moreover, $C_{\Phi}$ is unitary on $\mathcal{A}_{\alpha}^2(H)$ if and…

We find a lower bound for the essential norm of the difference of two composition operators acting on $H^2(B_N)$ or $A^2_s(B_N)$ ($s>-1$). This result plays an important role in proving a necessary and sufficient condition for the…

Let $\varphi$ be a linear-fractional, non-automorphism self-map of $\mathbb{D}$ that fixes $\zeta \in \mathbb{T}$ and satisfies $\varphi^{\prime}(\zeta) \neq 1$ and consider the composition operator $C_{\varphi}$ acting on the Hardy space…

Suppose $\mathcal{H}$ is a weighted Hardy space of analytic functions on the unit ball $\mathbb{B}_n\subset\mathbb{C}^n$ such that the composition operator $C_\psi$ defined by $C_{\psi}f=f\circ\psi$ is bounded on $\mathcal{H}$ whenever…

We characterize the analytic self-maps $\phi$ of the unit disk ${\Bbb D}$ in ${\Bbb C}$ that induce continuous composition operators $C_\phi$ from the log-Bloch space $\mathcal{B}^{\log}({\Bbb D})$ to $\mu$-Bloch spaces ${\mathcal…

Conditions for a composition operator on the Hardy space of the disk to have closed range or be similar to an isometry are well known. We provide such conditions for composition operators on the Hardy space of the upper half-plane. We also…

Let {\phi} be an analytic self-map of D and be an analytic operator-valued function on D, where D is the unit disk. We provide necessary and sufficient conditions for the boundedness and compactness of weighted composition operators…

In the present paper, we study the composition operators acting on weighted Hardy spaces of polynomial growth, which are concerned with norms, spectra and (semi-)Fredholmness. Firstly, we estimate the norms of the composition operators with…

In this work, we prove that weak compactness of composition operator on $H^{1}(U^{n})$ coincides with its compactness. We also characterize bounded and compact composition operators on $H^{1}(U^{n}).$\

Let $U^{n}$ be the unit polydisc of ${\Bbb C}^{n}$ and $\phi=(\phi_1, >..., \phi_n)$ a holomorphic self-map of $U^{n}.$ By ${\cal B}^p(U^{n})$, ${\cal B}^p_{0}(U^{n})$ and ${\cal B}^p_{0*}(U^{n})$ denote the $p$-Bloch space, Little…

The classical Littlewood's theorem establishes boundedness and provides a norm estimate for composition operators on the Hardy space. In this paper, we offer an alternative proof of boundedness and derive a new norm estimate that improves…

When \ph\ is an analytic self-map of the unit disk with Denjoy-Wolff point $a \in \D$, and $\rho(\W) = \psi(a)$, we give an exact characterization for when \W\ is normaloid. We also determine the spectral radius, essential spectral radius,…

In this paper, we investigate the compactness of the commutator $[C_\psi^{\ast}, C_\varphi]$ on the Hardy space $H^2(B_N)$ or the weighted Bergman space $A^2_s(B_N)$ ($s>-1$), when $\varphi$ and $\psi$ are automorphisms of the unit ball…

This paper gives some simple estimates of the essential norm for the difference of composition operators induced by $\phi$ and $\psi$ acting on bounded function space in the unit polydiscs $U^n$, where $\phi(z)$ and $\psi(z)$be holomorphic…

We obtain some estimates for norm and essential norm of the difference of two composition operators between weighted Bergman spaces $A^p_\alpha$ and $A^q_\beta$ on the unit ball. In particular, we completely characterize the boundedness and…

In this paper, we investigate the complex symmetric structure of generalized weighted composition operators $D_{m,\psi,\varphi}$ on the weighted Hardy space $H^2(\beta)$. We obtain explicit conditions for $ D_{m,\psi,\varphi}$ to be complex…

We give some new estimates for the norm and essential norm of a weighted composition operator on the Bloch space. As corollaries, we obtain some new characterizations of the boundedness and compactness of a weighted composition operator on…