Related papers: Weakly almost periodic functionals, representation…

We introduce and study the class of weak almost limited operators. We establish a characterization of pairs of Banach lattices $E$, $F$ for which every positive weak almost limited operator $T:E\rightarrow F$ is almost limited (resp. almost…

Let $p\in[1,\infty]$. Being motivated by weakly $p$-convergent and weak$^\ast$ $p$-convergent operators between Banach spaces introduced by Fourie and Zeekoei, we introduce and study the classes of weakly $p$-convergent and weak$^\ast$…

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…

For an operator T from X to Y denote m(T) the infimum of $||Tx||$ on the unit sphere $S_X$ of X. A sequence $(x_n)$ in $S_X$ is said to be minimizing for T if $||Tx_n||$ tends to m(T). In 2020 U. S. Chakraborty introduced and studied the…

We introduce a measure of super weak noncompactness $\Gamma$ defined for bounded linear operators and subsets in Banach spaces that allows to state and prove a characterization of the Banach spaces which are subspaces of a Hilbert generated…

The notion of super weak compactness for subsets of Banach spaces is a strengthening of the weak compactness that can be described as a local version of super-reflexivity. A recent result of K. Tu which establishes that the closed convex…

We introduce new class of limitedly L-weakly compact operators from a Banach space to a Banach lattice. This class is a proper subclass of the Bourgain-Diestel operators and it contains properly the class of L-weakly compact operators. We…

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…

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…

For a compact group $\mathbb{G}$, the functor from unital Banach algebras with contractive morphisms to metric spaces with 1-Lipschitz maps sending a Banach algebra $A$ to the space of $\mathbb{G}$-representations in $A$ preserves filtered…

In this paper we study the reflexivity of a unital strongly closed algebra of operators with complemented invariant subspace lattice on a Banach space. We prove that if such an algebra contains a complete Boolean algebra of projections of…

We survey recent results about composition operators induced by analytic self-maps of the unit disk in the complex plane on various Banach spaces of analytic functions taking values in infinite-dimensional Banach spaces. We mostly…

Let $X_1, \ldots, X_m$ be Banach spaces and let $E_1, \ldots, E_m,F$ be Banach lattices. Our main results read as follows: (i) The linear adjoint $A^*$ of a continuous multilinear operator $A \colon X_1 \times \cdots \times X_m \to F$ is…

In this paper, we introduce the concept of a pseudo weakly compact operator of order $ p $ between Banach spaces. Also we study the notion of $ p $-Dunford-Pettis relatively compact property which is in "general" weaker than the…

A classical result by R. Rochberg says that every bounded Toeplitz operator $T$ on the Hilbert Paley-Wiener space $\mathrm{PW}_a^2$ admits a bounded symbol $\varphi$. We generalize this result to Toeplitz operators on the Banach…

In this paper we give a various conditions for which the tuple $\mathcal{T} = (T_{1} , T_{2} , ... , T_{n})$ of commutative bounded linear operators on an infinite dimensional ( real , complex ) Banach space X is orbit reflexive. After we…

Let $A$ be a Banach algebra. For $f\in A^{\ast}$, we inspect the weak sequential properties of the well-known map $T_f:A\to A^{\ast}$, $T_f(a) = fa$, where $fa\in A^{\ast}$ is defined by $fa(x) = f(ax)$ for all $x\in A$. We provide…

Every absolutely summing linear operator is weakly compact. However, for strongly summing multilinear operators and polynomials - one of the most natural extensions of the linear case to the non linear framework - weak compactness does not…

In this paper, we present some necessary and sufficient conditions for semi-compact operators being almost L-weakly compact (resp. almost M-weakly compact) and the converse. Mainly, we prove that if $X$ is a nonzero Banach space, then every…

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…