Related papers: Composition operators from logarithmic Bloch space…
We consider continuous semigroups of analytic functions $\{\Phi_t\}_{t\geq0}$ in the so-called Gordon-Hedenmalm class $\mathcal{G}$, that is, the family of analytic functions $\Phi:\mathbb C_+\to \mathbb C_+$ giving rise to bounded…
A characterization of those points in the unit disc which belong to the spectrum of a composition operator $C_{\varphi}$, defined by a rotation $\varphi(z)=rz$ with $|r|=1$, on the space $H_0(\mathbb{D})$ of all analytic functions on the…
Let $H(\mathbb{B})$ denote the space of all holomorphic functions on the unit ball $\mathbb{B}\in \mathbb{C}^n$. In this paper we investigate the boundedness and compactness of the products of radial derivative operator and the following…
Let $B_d$ denote the unit ball of $\mathbb{C}^d$, $d\ge 1$. Given a holomorphic function $\varphi: B_d \to B_1$, we study the corresponding family $\sigma_\alpha[\varphi]$, $\alpha\in\partial B_1$, of Clark measures on the unit sphere…
The spectra of invertible weighted composition operators $uC_\varphi$ on the Bloch and Dirichlet spaces are studied. In the Bloch case we obtain a complete description of the spectrum when $\varphi$ is a parabolic or elliptic automorphism…
Let $\mathbb{B}$ be the unit ball of a complex Banach space $X$. In this paper, we will generalize the Bloch-type spaces and the little Bloch-type spaces to the open unit ball $\mathbb{B}$ by using the radial derivative. Next, we define an…
In this paper, we study 2-complex symmetric composition operators with the conjugation $J$ on the Hardy space $H^2$. More precisely, we obtain the necessary and sufficient condition for the composition operator $C_\phi$ to be 2-complex…
We study the Lipschitz continuity of pluriharmonic Bloch mappings in the unit ball $\mathbb{B}^n$ with respect to the Bergman metric. We apply this to obtain a sufficient condition such that the composition operator on the pluriharmonic…
Let $\Omega$ be a subdomain of $\mathbb{C}$ and let $\mu$ be a positive Borel measure on $\Omega$. In this paper, we study the asymptotic behavior of the eigenvalues of compact Toeplitz operator $T_\mu$ acting on Bergman spaces on $\Omega$.…
For any analytic self-map $\psi$ of $\{z: |z| < 1\}$, J. H. Shapiro has established that the square of the essential norm of the composition operator $C_\psi$ on the Hardy Space $H^2$ is precisely $\limsup_{|w|\rightarrow…
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)…
The Hilbert spaces $\mathscr{H}_{w}$ consisiting of Dirichlet series $F(s)=\sum_{ n = 1}^\infty a_n n^{ -s }$ that satisfty $\sum_{ n=1 }^\infty | a_n |^2/ w_n < \infty$, with $\{w_n\}_n$ of average order $\log_j n$ (the $j$-fold logarithm…
We study composition operators of characteristic zero on weighted Hilbert spaces of Dirichlet series. For this purpose we demonstrate the existence of weighted mean counting functions associated with the Dirichlet series symbol, and provide…
We study the boundedness of composition operators on the weighted Bergman spaces and the Hardy space over the polydisc. For arbitrary polydisc we prove the rank sufficiency theorem which, in particular, provides us with a simple criterion…
We first consider some questions raised by N. Zorboska in her thesis. In particular she asked for which sequences $\beta$ every symbol $\varphi \colon \mathbb{D} \to \mathbb{D}$ with $\varphi \in H^2 (\beta)$ induces a bounded composition…
In geometry group theory, one of the milestones is M. Gromov's polynomial growth theorem: Finitely generated groups have polynomial growth if and only if they are virtually nilpotent. Inspired by M. Gromov's work, we introduce the growth…
In this paper we initiate the study of composition operators on the noncommutative Hardy space $H^2_{\bf ball}$. Several classical results about composition operators (boundedness, norm estimates, spectral properties, compactness,…
The purpose of this paper is to describe the characterization for the compact difference of two composition operators acting between analytic Besov spaces and the weighted little Bloch type space over the unit disk.
In this paper we consider composition operators on Harmonic-Bloch type spaces and we compute the spectrum of composition operators. Also, we characterize isometric composition operators on harmonic Bloch type spaces.
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…