Related papers: (Weak) compactness of Hankel operators on BMOA

We establish weak factorizations for a weighted Bergman space $A^p_{\a}$, with $1<p<\infty$, into two weighted Bergman spaces on the unit ball of $\C^n$. To obtain this result, we characterize bounded Hankel forms on weighted Bergman spaces…

In this note, we establish several results concerning the continuity (or weak convergence) of the complex Monge-Amp\`ere operator on compact Hermitian manifolds. At the end of this note, we find a weak solution of the complex Monge-Amp\`ere…

We prove, under certain conditions, the existence of zeros for a weakly continuous operator on a paracompact topological space into the dual of a Banach space.

The boundedness of the small Hankel operator $h_f^\nu(g)=P_\nu(f\bar{g})$, induced by an analytic symbol $f$ and the Bergman projection $P_\nu$ associated to $\nu$, acting from the weighted Bergman space $A^p_\om$ to $A^q_\nu$ is…

We study the representation of non-weakly compact operators between $AL$-spaces. In this setting, we show that every operator admits a best approximant in the ideal of weakly compact operators. Using duality arguments, we extend this result…

We characterize, using time-frequency analysis, the continuity and compactness of the Weyl operator in global classes of ultradifferentiable functions $\mathcal{S}_\omega$, for weight functions $\omega$ in the sense of Braun, Meise and…

In this paper, we study the product of a Hankel operator and a Toeplitz operator on the Hardy space. We give necessary and sufficient conditions of when such a product $H_f T_g$ is compact.

For a wide class of unbounded integral Hankel operators on the positive half-line, we prove essential self-adjointness on the set of smooth compactly supported functions.

We study the boundedness of Hankel operators between two weighted spaces, with Muckenhoupt weights. In particular, we consider whether the Reproducing Kernel Thesis for Hankel operators generalizes to the case of two different weights.…

In this paper we solve a long standing problem about the bilinear $T1$ theorem to characterize the (weighted) compactness of bilinear Calder\'{o}n-Zygmund operators. Let $T$ be a bilinear operator associated with a standard bilinear…

A set of bounded linear operators from a Banach space to a Banach lattice is collectively L-weakly compact whenever union of images of the unit ball is L-weakly compact. We extend the Meyer-Nieberg duality theorem to collectively L-weakly…

We continue our study of operator algebras with contractive approximate identities (cais) by presenting a couple of interesting examples of operator algebras with cais, which in particular answer questions raised in previous papers in this…

We characterize super weakly compact operators as those through which binary tree and diamond and Laakso graphs may not be factored with uniform distortion.

Motivated by the equivalent definition of a continuous operator between Banach spaces in terms of weakly null nets, we introduce two types of continuous operators between Banach lattices using unbounded absolute weak convergence. We…

We provide martingale analogs of weakly cancelling differential operators and prove a Sobolev-type embedding theorem for these operators in the martingale setting.

We prove a Hankel-variant commutant lifting theorem. This also uncovers the complete structure of the Beurling-type reducing and invariant subspaces of Hankel operators. Kernel spaces of Hankel operators play a key role in the analysis.

We describe a new representation of Hankel operators $H$ as pseudo-differential operators $A$ in the space of functions defined on the whole axis. The amplitudes of such operators $A$ have a very special structure: they are products of…

We study big Hankel operators acting on vector-valued Fock spaces with radial weights in $\C^d$. We provide complete characterizations for the boundedness, compactness and Schatten class membership of such operators.

We prove a weak-type estimate for a class of operators extending some of the almost orthogonality issues involved in the study of the bilinear Hilbert transform by Lacey and Thiele.

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…