Related papers: A Bloch type space associated with {\lambda}-analy…

Let $\calH$ be a separable infinite-dimensional $\C$-linear Hilbert space, with sesquilinear inner product $\langle\cdot,\cdot\rangle_\calH$. Given any two orthonormal systems $x_1,x_2,x_3,\ldots$ and $y_1,y_2,y_3,\ldots$ in $\calH$, we…

This paper aims to determine the predual of the Bergman space $A_\lambda^1$ on the Siegel upper half-space. To achieve this, a Bloch-type space $\widetilde{\calB}$ is introduced and studied, and some of its essential properties are…

Every analytic self-map of the unit ball of a Hilbert space induces a bounded composition operator on the space of Bloch functions. Necessary and sufficient conditions for compactness of such composition operators are provided, as well as…

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 $S$ a contractive analytic operator-valued function on the unit disk ${\mathbb D}$, de Branges and Rovnyak associate a Hilbert space of analytic functions ${\mathcal H}(S)$. A companion survey provides equivalent definitions and basic…

The goal of the present paper is to introduce and study noncommutative Hardy spaces associated with the regular $\Lambda$-polyball, to develop a functional calculus on noncommutative Hardy spaces for the completely non-coisometric (c.n.c.)…

We introduce the Schur class of functions, discrete analytic on the integer lattice in the complex plane. As a special case, we derive the explicit form of discrete analytic Blaschke factors and solve the related basic interpolation…

A consistent description of images on the disk and of their transformations is given as elements of a vector space and of an operators algebra. The vector space of images on the disk $\mathbb{D}$ is the Hilbert space $L^2(\mathbb{D})$ that…

In this paper we investigate an interesting subclass $\mathcal{BS}(\alpha)$ ($0\leq \alpha<1$) of starlike functions in the unit disk $\Delta$. The class $\mathcal{BS}(\alpha)$ was introduced by Kargar et al. [R. Kargar, A. Ebadian and J.…

For normalised analytic functions $f$ defined on the open unit disc $\mathbb{D}$ satisfying the condition $\sup_{z\in \mathbb{D}}(1-|z^2|) |f'(z)|\leq 1$, known as Bloch functions, we determine various starlikeness radii.

Let $({\mathcal X}, d, \mu)$ be a metric measure space and satisfy the so-called upper doubling condition and the geometrically doubling condition. In this paper, the authors introduce the space ${\mathop\mathrm{RBLO}}(\mu)$ and prove that…

We introduce the Banach spaces $\ell^p_{a,b}$ and $c_{0,a,b}$, of analytic functions on the unit disc, having normalized Schauder bases consisting of polynomials of the form $f_n(z)=(a_n+b_nz)z^n, ~~n\geq0$, where $\{f_n\}$ is assumed to be…

Let $E$ be the open unit disk $\{z\in \mathbb{C}: |z|<1\}$. Let $A$ be the class of analytic functions in $E$, which have the form $f(z)=z+a_2z^2+...$. We define operators $L_n^\sigma\colon A\to A$ using the convolution *. Using these…

When the weight $\mu$ is more general than normal, the complete characterizations in terms of the symbol $g$ and weights for the conditions of the boundedness and compactness of $T_g: H^{\infty}_\nu\rightarrow H^{\infty}_\mu$ and $S_g:…

For $\sigma>0$, the Bernstein space \ $B^1_{\sigma}$ consists of those $L^1(R)$\ functions whose Fourier transforms are supported by $[-\sigma,\sigma]$. Since $B^1_{\sigma}$ is separable and dual to some Banach space, the closed unit ball…

We study certain densely defined unbounded operators on the Segal-Barg\-mann space, related to the annihilation and creation operators of quantum mechanics. We consider the corresponding $D$-complex and study properties of the corresponding…

If $\mu $ is a positive Borel measure on the interval $[0, 1)$ we let $\mathcal H_\mu $ be the Hankel matrix $\mathcal H_\mu =(\mu_{n, k})_{n,k\ge 0}$ with entries $\mu_{n, k}=\mu_{n+k}$, where, for $n\,=\,0, 1, 2, \dots $, $\mu_n$ denotes…

A broader class of Hardy spaces and Lebesgue spaces have been introduced recently on the unit circle by considering continuous $\|.\|_1$-dominating normalized gauge norms instead of the classical norms on measurable functions and a Beurling…

We consider Toeplitz operators in Bergman and Fock type spaces of polyanalytic $L^2\textup{-}$functions on the disk or on the half-plane with respect to the Lebesgue measure (resp., on $\mathbb{C}$ with the plane Gaussian measure). The…

We show that the space of bounded and linear operators between spaces of continuous functions on compact Hausdorff topological spaces has the Bishop-Phelps-Bollob\'as property. A similar result is also proved for the class of compact…