Related papers: Bounded convergence theorems

Let E be a topological space and F a uniform space. We introduce a new topology (in fact a uniform structure) called the V-congergence on the space of applications from E to F such that C(E,F) is closed for this topology and the restriction…

Following several papers in the prior literature, we study the relationship between order bounded operators, topologically bounded operators and topologically continuous operators. Our main contribution is two folded: (i) we provide a set…

The purpose of this paper is to study the approximation of vector valued mappings defined on a subset of a normed space. We investigate Korovkin-type conditions under which a given sequence of linear operators becomes a so-called…

What is the correct noncommutative generalization of the functor $C_0(X) \mapsto \ell^\infty(X)$ for locally compact Hausdorff $X$ having a countable basis? Making the ansatz $K(\ell^2) \mapsto B(\ell^2)$, we expect that every unital…

We modify the very well known theory of normed spaces $(E, \norm)$ within functional analysis by considering a sequence $(\norm_n : n\in\N)$ of norms, where $\norm_n$ is defined on the product space $E^n$ for each $n\in\N$. Our theory is…

This article presents a deep investigation of fixed points for multivalued weak contractions in cone metric spaces. We extend Berinde weak contraction principles to the multivalued setting in cone metric spaces, developing existence,…

We introduce the concept of an $E$-valued function algebra, a type of Banach algebra that consist of continuous $E$-valued functions on some compact Hausdorff space, where $E$ is a Banach algebra. We present some basic results about such…

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 study power boundedness and related properties such as mean ergodicity for (weighted) composition operators on function spaces defined by local properties. As a main application of our general approach we characterize when (weighted)…

We introduce the post-processing preorder and equivalence relations for general measurements on a possibly infinite-dimensional general probabilistic theory described by an order unit Banach space $E$ with a Banach predual. We define the…

We prove a criterion for continuity of bilinear maps on countable direct sums of topological vector spaces. As a first application, we get a new proof for the fact (due to Hirai et al. 2001) that the map taking a pair of test functions on…

Let X be an L1-predual and E,F be Banach spaces. We use the fact that an unconditionally converging operator T from the injective tensor product of X and E to F is strongly bounded and extend T to an operator S on continuous F-valued…

In this article, the class of all Dunford-Pettis $ p $-convergent operators and $ p $-Dunford-Pettis relatively compact property on Banach spaces are investigated. Moreover, we give some conditions on Banach spaces $ X $ and $ Y $ such that…

In this paper, we introduce statistical bounded set on topological vector space. Also, we consider three classes of bounded operators from topological vector spaces to ordered topological vector spaces. Moreover, we give relations between…

In this paper we consider a generalized version of bounded oscillation operators, involving new parameters in the definition, as well as considering the operators on vector-valued function spaces. With this definition we will capture some…

We introduce certain linear positive operators and study some approximation properties of these operators in the space of functions, continuous on a compact set, of two variables. We also find the order of this approximation by using…

We prove that, any problem of minimization of proper lower semicontinuous function defined on a normal Hausdorff space, is canonically equivalent to a problem of minimization of a proper weak * lower semicontinuous convex function defined…

The Egoroff theorem for measurable $\bold X$-valued functions and operator-valued measures $\bold m: \Sigma \to L(\bold X, \bold Y)$, where $\Sigma$ is a $\sigma$-algebra of subsets of $T \neq \emptyset$ and $\bold X$, $\bold Y$ are both…

We study the class of compact convex subsets of a topological vector space which admits a strictly convex and lower semicontinuous function. We prove that such a compact set is embeddable in a strictly convex dual Banach space endowed with…

Let $X$ and $Y$ be the Hausdorff topological spaces and let $A$ be both an $\fs$- and $\gd$- subset of $X$. Let also $f\cn A\to Y$ be a function for which the inverse image of every open subset $U\subset Y$ is $\fs$ in $X$. We show that $f$…