Related papers: Weighted composition operators of $C_0(X)$'s

Suppose $X$ and $Y$ are locally compact Hausdorff spaces, $E$ and $F$ are Banach spaces and $F$ is strictly convex. We show that every linear isometry $T$ from $C_0(X,E)$ {\em into} $C_0(Y,F)$ is essentially a weighted composition operator…

Let $\mathrm{Lip}(X)$, $\mathrm{Lip}^b(X)$, $\mathrm{Lip}^{\mathrm{loc}}(X)$ and $\mathrm{Lip}^\mathrm{pt}(X)$ be the vector spaces of Lipschitz, bounded Lipschitz, locally Lipschitz and pointwise Lipschitz (real-valued) functions defined…

Let $\mathbb F$ be a finite field and let $\mathcal A$ and $\mathcal B$ be vector spaces of $\mathbb F$-valued continuous functions defined on locally compact spaces $X$ and $Y$, respectively. We look at the representation of linear…

Let $\epsilon >0$. A continuous linear operator $T:C(X) \ra C(Y)$ is said to be {\em $\epsilon$-disjointness preserving} if $\vc (Tf)(Tg)\vd_{\infty} \le \epsilon$, whenever $f,g\in C(X)$ satisfy $\vc f\vd_{\infty} =\vc g\vd_{\infty} =1$…

It is proved that every linear biseparating map between spaces of vector-valued differentiable functions is a weighted composition map. As a consequence, such a map is always continuous.

The main problem considered in this article is the following: if $\mathbf{F}$, $\mathbf{E}$ are normed spaces of continuous functions over topological spaces $X$ and $Y$ respectively, and $\omega:Y\to\mathbb{C}$ and $\Phi:Y\to X$ are such…

Let $X$ and $Y$ be compact Hausdorff spaces, and let $C(X)$ and $C(Y)$ denote the commutative Banach algebras of all continuous complex-valued functions on $X$ and $Y$, respectively. We study bijective maps $T$ from $C(X)$ onto $C(Y)$ which…

Given pointed metric spaces $X$ and $Y$, we characterize the basepoint-preserving Lipschitz maps $\phi$ from $Y$ to $X$ inducing an isometric composition operator $C_\phi$ between the Lipschitz spaces $Lip_0(X)$ and $Lip_0(Y)$, whenever $X$…

This paper studies the behaviour of iterates of weighted composition operators acting on spaces of analytic functions, with particular emphasis on the Hardy space $H^2$. Questions relating to uniform, strong and weak convergence are…

Let $\phi$ be an analytic self-map and $u$ be a fixed analytic function on the open unit disk $D$ in the complex plane $\CC.$ The weighted composition operator is defined\break by \begin{equation*} uC_\phi f =u \cdot (f\circ \phi), f \in…

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…

Let $X, Y$ be complete metric spaces and $E, F$ be Banach spaces. A bijective linear operator from a space of $E$-valued functions on $X$ to a space of $F$-valued functions on $Y$ is said to be biseparating if $f$ and $g$ are disjoint if…

We provide a complete description of the spectrum and the essential spectra of weighted composition operators $T=wT_\varphi$ on $C(K)$ in the case when the map $\varphi$ is a non-invertible homeomorphism of $K$ into itself.

In this paper, we study the weighted composition operator on the Fock space $\mf$ of slice regular functions. First, we characterize the boundedness and compactness of the weighted composition operator. Subsequently, we describe all the…

We study the weighted composition operators between the Lipschitz space and the space of bounded functions on the set of vertices of an infinite tree. We characterized the boundedness, the compactness, and the boundedness from below of…

In this paper we obtain characterizations for adjoint of a composition and weighted composition operator to be composition and weighted composition operator on $F_{\psi}^2,$ respectively. We study the co-isometry composition and weighted…

We obtain criteria for the boundedness and compactness of weighted composition operators between different Fock spaces in $\mathbb{C}^n$. We also give estimates for essential norm of these operators.

We study weighted composition operators acting between Fock spaces. The following results are obtained: (1) Criteria for the boundedness and compactness; (2) Characterizations of compact differences and essential norm; (3) Complete…

A bounded linear operator $T$ on a separable complex Hilbert space $H$ is called $C$-normal if there is a conjugation $C$ on $H$ such that $ CT^\ast TC=TT^\ast$. Let $\varphi$ be a linear fractional self-map of $\mathbb{D}$. In this paper,…

Let $X=(X,\mathcal{B},\mu)$ be a $\sigma$-finite measure space and \mbox{$f:X\to X$} be a measurable transformation such that the composition operator $T_f:\varphi\mapsto \varphi\circ f$ is a bounded linear operator acting on…