Related papers: Some results on isometric composition operators on…

We investigate the relationship between the complex symmetry of composition operators $C_{\phi}f=f\circ \phi$ induced on the classical Hardy space $H^2(\mathbb{D})$ by an analytic self-map $\phi$ of the open unit disk $\mathbb{D}$ and its…

We give examples of composition operators $C\_\Phi$ on $H^2 (\D^2)$ showing that the condition $\|\Phi \|\_\infty = 1$ is not sufficient for their approximation numbers $a\_n (C\_\Phi)$ to satisfy $\lim\_{n \to \infty} [a\_n (C\_\Phi)…

For suitable bounded hyperconvex sets $\Omega$ in $\mathbb{C}^N$, in particular the ball or the polydisk, we give estimates for the approximation numbers of composition operators $C_\phi \colon H^2 (\Omega) \to H^2 (\Omega)$ when $\phi…

A complete characterisation is given of all the linear isometries of the Fr\'echet space of all holomorphic functions on the unit disc, when it is given one of the two standard metrics: these turn out to be weighted composition operators of…

We study a composition operator on Lorentz spaces. In particular we provide necessary and sufficient conditions under which a measurable mapping induces a bounded composition operator.

We consider weighted composition operators, that is operators of the type $g \mapsto w \cdot g \circ f$, acting on spaces of Lipschitz functions. Bounded weighted composition operators, as well as some compact weighted composition…

In this paper, we provide an infinite metric space $M$ such that the set $\mbox{SNA}(M)$ of strongly norm-attaining Lipschitz functions does not contain a subspace which is isometric to $c_0$. This answers a question posed by Antonio…

We investigate some types of composition operators, linear and not, and conditions for some spaces to be mapped into themselves and for the operators to satisfy some good properties.

We prove that the weighted composition operator $W_{\phi,\varphi}$ fixes an isomorphic copy of $\ell^p$ if the operator $W_{\phi,\varphi}$ is not compact on the derivative Hardy space $S^p$. In particular, this implies that the strict…

In this study, we investigate the boundedness of composition operators acting on Morrey spaces and weak Morrey spaces. The primary aim of this study is to investigate a necessary and sufficient condition on the boundedness of the…

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…

In this article, we completely characterize the complex symmetry, cyclicity and hypercyclicity of composition operators $C_\phi f=f\circ\phi$ induced by affine self-maps $\phi$ of the right half-plane $\mathbb{C}_+$ on the Hardy-Hilbert…

Let $\varphi$ be a self-map of the unit disk and let $C_\varphi$ denote the composition operator acting on the standard Dirichlet space $\mathcal{D}$. A necessary condition for compactness of a difference of two bounded composition…

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 study $M$-ideals of compact operators by means of the property~$(M)$ introduced in \cite{Kal-M}. Our main result states for a separable Banach space $X$ that the space of compact operators on $X$ is an $M$-ideal in the space of bounded…

Let $\Phi:TM\to TM$ be a positive-semidefinite symmetric operator of class $C^1$ defined on a complete non-compact manifold $M$ isometrically immersed in a Hadamard space $\bar{M}$. In this paper, we given conditions on the operator $\Phi$…

We investigate composition operators $C_{\Phi}$ on the Hardy-Smirnov space $H^{2}(\Omega)$ induced by analytic self-maps $\Phi$ of an open simply connected proper subset $\Omega$ of the complex plane. When the Riemann map…

We compare the compactness of composition operators on $H^2$ and on Orlicz-Hardy spaces $H^\Psi$. We show in particular that exists an Orlicz function $\Psi$ such that $H^{3+\eps} \subseteq H^\Psi \subseteq H^3$ for every $\eps >0$, and a…

For certain weighted locally convex spaces $X$ and $Y$ of one real variable smooth functions, we characterize the smooth functions $\varphi: \mathbb{R} \to \mathbb{R}$ for which the composition operator $C_\varphi: X \to Y, \, f \mapsto f…

We solve two main questions on linear structures of (non-)norm-attaining Lipschitz functions. First, we show that for every infinite metric space $M$, the set consisting of Lipschitz functions on $M$ which do not strongly attain their norm…