Related papers: Composition operators for holomorphic Lipschitz fu…
We give a complete characterization of the spectrum of composition operators, induced by an automorphism of the open unit disk, acting on a family of Banach spaces of analytic functions that includes the Bloch space and BMOA. We show that…
In this paper, we establish bounds on the norm of multiplication operators on the Bloch space of the unit disk via weighted composition operators. In doing so, we characterize the isometric multiplication operators to be precisely those…
The algebra of Dirichlet series $\mathcal{A}(\mathcal{C}_{+})$ consists on those Dirichlet series convergent in the right half-plane $\mathcal{C}_{+}$ and which are also uniformly continuous there. This algebra was recently introduced by…
We consider the products of composition and differentiation operators on the Hardy space. We provide a complete characterization of the boundedness and compactness of these operators. Furthermore, we obtain the explicit condition for these…
Let $\varphi$ be a holomorphic self-map of a bounded homogeneous domain $D$ in $\mathbb{C}^n$. In this work, we show that the composition operator $C_\varphi: f\mapsto f\circ \varphi$ is bounded on the Bloch space $\mathcal{B}$ of the…
We study the existence of continuous (linear) operators from the Banach spaces $\mbox{Lip}_0(M)$ of Lipschitz functions on infinite metric spaces $M$ vanishing at a distinguished point and from their predual spaces $\mathcal{F}(M)$ onto…
Here, the composition operators on Orlicz spaces with finite ascent and descent as well as infinite ascent and descent are characterized.
In this paper, we study the differentiation operator acting on discrete function spaces; that is spaces of functions defined on an infinite rooted tree. We discuss, through its connection with composition operators, the boundedness and…
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 study best approximations to compact operators between Banach spaces and Hilbert spaces, from the point of view of Birkhoff-James orthogonality and semi-inner-products. As an application of the present study, some distance formulae are…
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.
Let $\phi$ and $\psi$ be holomorphic self-maps of the unit polydisc $U^n$ in the $n$-dimensional complex space, and denote by $C_{\phi}$ and $C_{\psi}$ the induced composition operators. This paper gives some simple estimates of the…
The aim of this article is to detect the ascent and descent of weighted composition operators on Lorentz spaces. We investigate the conditions on the measurable transformation $T$ and the complex-valued measurable function $u$ defined on…
A necessary and sufficient condition for an operator space to support a multiplication making it completely isometric and isomorphic to a unital operator algebra is proved. The condition involves only the holomorphic structure of the Banach…
Many iterative optimization algorithms involve compositions of special cases of Lipschitz continuous operators, namely firmly nonexpansive, averaged and nonexpansive operators. The structure and properties of the compositions are of…
Recently, in arXiv:2304.07149, a bridge was made between the very active area of spaces of Lipschitz real functions on a metric space and holomorphic functions on an open subset of a Banach space. This was done by introducing and studying…
In this paper, we specify what functions induce the bounded composition operators on a reproducing kernel Hilbert space (RKHS) associated with an analytic positive definite function defined on $\mathbf{R}^d$. We prove that only affine…
In the context of analytic functions on the open unit disk, a weighted composition operator is simply a composition operator followed by a multiplication operator. The class of weighted composition operators has an important place in the…
We observe that local embedding problems for certain Hardy and Bergman spaces of Dirichlet series are equivalent to boundedness of a class of composition operators. Following this, we perform a careful study of such composition operators…
We consider compact composite linear operators in Hilbert space, where the composition is given by some compact operator followed by some non-compact one possessing a non-closed range. Focus is on the impact of the non-compact factor on the…