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

For two commuting Tonelli Hamiltonians, we recover the commutation of the Lax-Oleinik semi-groups, a result of Barles and Tourin ([BT01]), using a direct geometrical method (Stoke's theorem). We also obtain a "generalization" of a theorem…

We study order-to-weak continuous operators from an ordered Banach space to a normed space. It is proved that under rather mild conditions every order-to-weak continuous operator is bounded.

We show that for $f$ a continuous function on the closed polydisc $\bar{\mathbb{D}^n}$ with $n\geq 2$, the Hankel operator $H_{f}$ is compact on the Bergman space of $\mathbb{D}^n$ if and only if there is a decomposition $f=h+g$, where $h$…

This paper characterises the boundedness and compactness of Agler--McCarthy monomial operators by reducing them to weighted composition operators and deriving explicit Carleson measure criteria on the half-plane. The results are illustrated…

We introduce and study in a general setting the concept of homogeneity of an operator and, in particular, the notion of homogeneity of an integral operator. In the latter case, homogeneous kernels of such operators are also studied. The…

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We prove several singular value inequalities for sum and product of compact operators in Hilbert space. Some of our results generalize the previous inequalities for operators. Also, applications of some inequalities are given.

A locally compact groupoid is said to have the weak containment property if its full $C^*$-algebra coincides with its reduced one. This property is strictly weaker than amenability and is known to be equivalent to amenability for…

In a previous paper, we obtained several "compact versions" of Rubio de Francia's weighted extrapolation theorem, which allowed us to extrapolate the compactness of linear operators from just one space to the full range of weighted Lebesgue…

Let $T:Y\to X$ be a bounded linear operator between two normed spaces. We characterize compactness of $T$ in terms of differentiability of the Lipschitz functions defined on $X$ with values in another normed space $Z$. Furthermore, using a…

In this paper we characterize quasi-contraction, stable and convergent weighted conditional type (WCT) operators on $L^p(\mu)$. Indeed we provide equivalent conditions for quasi-contraction WCT operators. Also, we prove that convergence,…

Higher-order abstract GSOS is a recent extension of Turi and Plotkin's framework of Mathematical Operational Semantics to higher-order languages. The fundamental well-behavedness property of all specifications within the framework is that…

Let $\Omega$ be a bounded pseudoconvex domain in $\mathbb{C}^2$ with Lipschitz boundary or a bounded convex domain in $\mathbb{C}^n$ and $\phi\in C(\overline{\Omega})$ such that $H_{\phi}$ is compact on $A^2(\Omega)$. Then $\phi\circ f$ is…

It has been very recently discovered that there are compact linear operators between Banach spaces which cannot be approximated by norm attaining operators. The aim of this expository paper is to give an overview of those examples and also…

We give orthonormal characterizations of collectively compact (limited) sets of linear operators from a Hilbert space to a Banach space.

We establish the characterization of compactness for the sparse operator (associated with symbol in weighted VMO space) in the two weight setting on the spaces of homogeneous type in the sense of Coifman and Weiss. As a direct application…

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In this paper we characterize some basic properties of composition operators on the spaces of harmonic Bloch functions. First we provide some equivalent conditions for boundedness and compactness of composition operators. Then by using…

We obtain a complete characterization of the weak-type $(1,1)$ for Haar shift operators in terms of generalized Haar systems adapted to a Borel measure $\mu$ in the operator-valued setting. The main technical tool in our method is a…

A continuous operator $T$ between two Banach lattices $E$ and $F$ is called almost order-weakly compact, whenever for each almost order bounded subset $A$ of $E$, $T(A)$ is a relatively weakly compact subset of $F$. In Theorem 4, we show…