Rigidity of weighted composition operators on H^p

The topological structure of the set of (weighted) composition operators has been studied on various function spaces on the unit disc such as Hardy spaces, the space of bounded holomorphic functions, weighted Banach spaces of holomorphic functions with sup-norm, Hilbert Bergman spaces. In this paper we consider this problem for all Bergman spaces $$A_{\alpha }^p$$ with $$p \in (0, \infty )$$ and $$ \alpha \in (-1, \infty )$$ . In this setting we establish a criterion for two composition operators to be linearly connected in the space of composition operators; furthermore, for the space of weighted composition operators, we prove that the set of compact weighted composition operators is path connected, but it is not a component.

In this paper, we investigate when weighted composition operators acting on Dirichlet spaces [Formula: see text] are complex symmetric with respect to some special conjugations. We then provide some characterizations of Hermitian weighted composition operators on [Formula: see text]. Furthermore, we give a sufficient and necessary condition for [Formula: see text]-symmetric weighted composition operators on Hardy spaces [Formula: see text] to be unitary or Hermitian, then some new examples of complex symmetric weighted composition operators on [Formula: see text] are obtained. We also discuss the normality of complex symmetric weighted composition operators on [Formula: see text].

Weighted composition operators between Hardy and growth spaces on the upper half-plane

We characterize bounded and compact weighted composition operators acting between weighted Bergman spaces and between Hardy spaces. Our results use certain integral transforms that generalize the Berezin transform. We also estimate the essential norms of these operators. As applications, we characterize bounded and compact pointwise multiplication operators between weighted Bergman spaces and estimate their essential norms.

In this paper we investigate weighted composition operators between weak and strong vector-valued Bergman spaces and Hardy spaces, and give some estimates of their norms.

Norms of multiplication operators on Hardy spaces and weighted composition operators from Hardy spaces to weighted-type spaces on bounded symmetric domains

Let X be a finite or infinite dimensional complex Banach space. We characterize the bounded weighted composition operators between the Bloch type space and the Hardy space on the unit ball of X, extending several known results for finite dimensional domains.

Suppose $\\varphi$ is an analytic self-map of open unit disk $\\mathbf{D}$ and $\\psi$ is an analytic function on $\\mathbf{D}$. Then a weighted composition operator induced by $\\varphi$ with weight $\\psi$ is given by $(W_{\\psi, \\varphi}f)(z)= \\psi(z)f(\\varphi(z))$, for $z \\in \\mathbf{D}$ and $f$ analytic on $\\mathbf{D}$. Necessary and sufficient conditions are given for the boundedness and compactness of the weighted composition operators $W_{\\psi, \\varphi}$. In terms of fixed points in the closed unit disk $\\overline{\\mathbf{D}}$, conditions under which $W_{\\psi, \\varphi}$ is compact are given. Necessary conditions for the compactness of $C_{\\varphi}$ are given in terms of the angular derivative $\\varphi^{\\prime}(\\zeta)$ where $\\zeta$ is on the boundary of the unit disk. Moreover, we present sufficient conditions for the membership of composition operators in the Schatten $p$-class $S_{p}(H^s(\\beta_1), H^q(\\beta_2))$, where the inducing map has supremum norm strictly smaller than~$1$.

We study the weighted composition operators Wh,φ on Hardy space \(H^2 (\mathbb{B})\) whenever h ∈ BMOA (resp. h ∈ VMOA). Analogous results are given for \(H^p (\mathbb{B})\) spaces and the scale of weighted Bergman spaces. In the latter case, BMOA is replaced by the Bloch space (resp. VMOA by the little Bloch space).

We study the bounded and the compact weighted composition operators from the Hardy space <TEX>$H^{\infty}$</TEX> into BMOA and into VMOA, from BMOA into <TEX>$H^{\infty}$</TEX>, as well as from BMOA into the Bloch space. We also provide new boundedness and compactness criteria for the weighted composition operators on BMOA and on VMOA.

This paper gives a note on weighted composition operators on the weighted Bergman space, which shows that for a fixed composition symbol, the weighted composition operators are bounded on the weighted Bergman space only with bounded weighted symbols if and only if the composition symbol is a finite Blaschke product.

We solve the closed range problem for weighted composition operators on Fock spaces. The result equivalently characterizes when the operators are bounded from below. We give several applications of the main result related to the operators invertibility, Fredholm, and dynamical sampling structures from frame perspectives. We prove there exists no vector in the Fock space for which its orbit under the weighted composition operator represents a frame family. Furthermore, it is shown that a weighted composition operator preserves frames if and only if it preserves the stronger Riesz basis property. Similar results are provided for the adjoint operator.

There are two aims in this paper. The first aim is to characterize the order-bounded weighted composition operators between Fock spaces, and the second is to further characterize the order-bounded difference in weighted composition operators between Fock spaces. At the same time, six examples are given to illustrate the relations between boundedness and ordered boundedness. Moreover, an interesting result is found that differences in weighted composition operators defined by some special weighted functions and symbol functions are order-bounded between Fock spaces if and only if each weighted composition operator is compact between Fock spaces. Finally, two open questions are also put forward for converting larger Fock spaces into smaller ones.

Information processing in the Block Design Task

Power bounded weighted composition operators on function spaces defined by local properties