Related papers: Bounded, compact and Schatten class Hankel operato…
An estimate for the norm of selfadjoint Toeplitz operators with a radial, bounded and integrable symbol is obtained. This emphasizes the fact that the norm of such operator is strictly less than the supremum norm of the symbol. Consequences…
A characterisation is given of bounded embeddings from weighted $L^2$ spaces on bounded intervals into $L^2$ spaces on the half-plane, induced by isomorphisms given by the Laplace transform onto weighted Hardy and Bergman spaces (Zen…
We generalize some results on compact operators on Hilbert spaces to "compact" operators on some Hilbert right W*-modules. We present in this frame the Schatten decomposition of the compact operators, the trace, the Banach Lp-spaces and…
In this paper we study the Bergman-Toeplitz operator $T_{\psi}$ induced by $\psi(w) = K_{\Omega}^{-\alpha}(w,w)d_{\Omega}^{\beta}(w)$ with $\alpha, \beta \geq 0$ acting from a weighted $L^p$-space $L_a^p(\Omega)$ to another one…
We determine the boundedness and compactness of a large class of operators, mapping from general Banach spaces of holomorphic functions into a particular type of spaces of functions determined by the growth of the functions, or the growth…
Unbounded (and bounded) Toeplitz operators (TO) with rational symbols are analysed in detail showing that they are densely defined closed and have finite dimensional kernels and deficiency spaces. The latter spaces as well as the domains,…
We introduce an ordinal index which characterizes weak compactness of operators between Banach spaces. We study when classes consisting of operators having bounded index form a closed ideal, the distinctness of the classes, and the…
We study Toeplitz operators on the Bargmann space, with Toeplitz symbols given by exponentials of complex quadratic forms. We show that the boundedness of the corresponding Weyl symbols is necessary for the boundedness of the operators,…
In this paper, we characterize the boundedness and the compactness of weighted composition operators acting on a de Branges-Rovnyak space $\mathcal H(b)$, where the symbol $b$ is a rational function in the unit ball of $H^\infty$ that is…
We obtain exhaustive results and treat in a unified way the question of boundedness, compactness, and weak compactness of composition operators from the Bloch space into any space from a large family of conformally invariant spaces that…
In this paper, we investigate the boundedness, compactness, essential norm and the Schatten class of weighted composition operators $uC_\varphi$ on Bergman type spaces $A_\omega^p $ with double weight $\omega$. Let $X=\{u\in H(D):…
The aim of the present paper is to define compact operators on asymmetric normed spaces and to study some of their properties. The dual of a bounded linear operator is defined and a Schauder type theorem is proved within this framework. The…
We study the holomorphic Hardy-Orlicz spaces H^\Phi(\Omega), where \Omega is the unit ball or, more generally, a convex domain of finite type or a strictly pseudoconvex domain in Cn . The function \Phi is in particular such that H…
This paper characterises the dual of the model space $K_I^1$, where $I$ is an inner function, intersected with the shifted Hardy space, $z H^1$. With this duality result, it is then shown that every bounded truncated Toeplitz operator on…
Ortega-Cerd\`a -- Seip demonstrated that there are bounded multiplicative Hankel forms which do not arise from bounded symbols. On the other hand, when such a form is in the Hilbert-Schmidt class $\mathcal{S}_2$, Helson showed that it has a…
$H^2\zProd$ denotes the Hardy space of square integrable functions analytic in each variable separately. Let $P^{\ominus}$ be the natural projection of $L^2\zProd$ onto $\z8{H^2\zProd}$. A Hankel operator with symbol $b$ is the linear…
We show that for an entire function $\varphi$ belonging to the Fock space ${\mathscr F}^2(\mathbb{C}^n)$ on the complex Euclidean space $\mathbb{C}^n$, the integral operator \begin{eqnarray*} S_{\varphi}F(z)=\int_{\mathbb{C}^n} F(w) e^{z…
Let $\mathbb{D}^n$ be the polydisk in $\mathbb{C}^n$ and the symbols $\phi,\psi\in C(\bar{\mathbb{D}^n})$ such that $\phi$ and $\psi$ are pluriharmonic on any $(n-1)$-dimensional polydisk in the boundary of $\mathbb{D}^{n}.$ Then…
In this paper we deal with the problem of describing the dual space $(B^1_\kappa)^*$ of the Bernstein space $B^1_\kappa$, that is the space of entire functions of exponential type at most $\kappa>0$ whose restriction to the real line is…
We prove an extrapolation of compactness theorem for operators on Banach function spaces satisfying certain convexity and concavity conditions. In particular, we show that the boundedness of an operator $T$ in the weighted Lebesgue scale…