Related papers: On the class of weak almost limited operators

In this paper we characterize the Banach lattices with the Hardy-Littlewood property by using maximal operators defined by semigroups of operators associated with the inverse Gauss measure.

For Fr{\'e}chet spaces E and F we write (E,F) \in {B} if every continuous linear operator from E to F is bounded. Let l be a Banach sequence space with a monotone norm in which the canonical system (e_{n}) is an unconditional basis. We…

We call a bounded linear operator acting between Banach spaces weakly compactly generated ($\mathsf{WCG}$ for short) if its range is contained in a weakly compactly generated subspace of its codomain. This notion simultaneously generalises…

We systematize and generalize recent results of Gerlach and Gl\"uck on the strong convergence and spectral theory of bounded (positive) operator semigroups $(T_s)_{s\in S}$ on Banach spaces (lattices). (Here, $S$ can be an arbitrary…

We consider weighted composition operators on spaces of analytic functions on the unit disc, which take values in some complex Banach space. We provide necessary and sufficient conditions for the boundedness and (weak) compactness of…

In this review we present some recent extensions of the method of the weakly conjugate operator. We illustrate these developments through examples of operators on graphs and groups.

In this short note, we show that one cannot differentiate between reciprocal Dunford--Pettis sets and V$^*$-sets in a Banach lattice. That is, for a bounded subset $K$ of a Banach lattice $E$, $K$ is a V$^*$-set if and only if $K$ is a…

Given a bilinear (or sub-bilinear) operator $B$, we prove restricted weighted weak type inequalities of the form $$ ||B(f_1, f_2)||_{L^{p, \infty}(w_1^{p/p_1}w_2^{p/p_2})}\lesssim ||f_1||_{L^{p_1, 1}(w_1)}||f_2||_{L^{p_2, 1}(w_2)}, $$…

In this paper, we study the notion of $\phi$-biflatness, $\phi$-biprojectivity, approximate biprojectivity and Johnson pseudo-contractibility for a new class of Banach algebras. Using this class of Banach algebras we give some examples…

We consider the two-dimensional Pauli operator perturbed by a weakly coupled, attractive potential. We show that besides the eigenvalues arising from the Aharonov-Casher zero modes there are two or one (depending on whether the flux of the…

In this paper, we explore the limiting weak-type behaviors of some integral operators including maximal operators, singular and fractional integral operators and maximal truncated singular integrals et al. Some optimal limiting weak-type…

This is a continuation of our earlier paper \cite{PT3}. We consider here operator-valued functions (or infinite matrix functions) on the unit circle $\T$ and study the problem of approximation by bounded analytic operator functions. We…

We introduce the concept of weak-localization for generalized frames and use this concept to define a class of weakly localized operators. This class contains many important operators, including: Short Time Fourier Transform multipliers,…

We introduce and study some operational quantities which characterize the disjointly non-singular operators from a Banach lattice $E$ to a Banach space $Y$ when $E$ is order continuous, and some other quantities which characterize the…

In this paper, we give simplified and equivalent characterizations of Banach limit functional, which is the minimum requirement to characterize strong almost convergence. With this machinery, we show that Hajdukovic's quasi-almost…

We study semigroups of bounded operators on a Banach space such that the members of the semigroup are continuous with respect to various weak topologies and we give sufficient conditions for the generator of the semigroup to be closed with…

Four possible definitions of the commutation relation $[S,T]=\Id$ of two closable unbounded operators $S,T$ are compared. The {\em weak} sense of this commutator is given in terms of the inner product of the Hilbert space $\H$ where the…

Let $K$ be an absolutely convex infinite-dimensional compact in a Banach space $\mathcal{X}$. The set of all bounded linear operators $T$ on $\mathcal{X}$ satisfying $TK\supset K$ is denoted by $G(K)$. Our starting point is the study of the…

Let A and B be bounded operators on a Banach lattice E such that the commutator C=AB-BA and the product BA are positive operators. If the product AB is a power-compact operator, then C is a quasi-nilpotent operator having a triangularizing…

Let $A$ be a bounded linear operator and $P$ a bounded linear projection on a Banach space $X$. We show that the operator semigroup $(e^{t(A-kP)})_{t \ge 0}$ converges to a semigroup on a subspace of $X$ as $k \to \infty$ and we compute the…