Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 29 October 2020Accepted: 26 August 2021Published online: November 2021Keywordsoptimal control infinite dimension, dynamic programming, state constraints, Hamilton--Jacobi--Bellman equation, Banach lattice, AK model economic growthAMS Subject Headings46B42, 49K27, 49L20, 9...

Motivated by an Arens regularity problem, we introduce the concepts of matrix Banach space and matrix Banach algebra. The notion of matrix normed space in the sense of Ruan is a special case of our matrix normed system. A matrix Banach algebra is a matrix Banach space with a completely contractive multiplication. We study the structure of matrix Banach spaces and matrix Banach algebras. Then we...

We prove some general results on sequential convergence in Frechet lattices that yield, as particular instances, the following regarding a closed ideal \(I\) of Banach lattice \(E\): (i) If two \(E\), and \(E/I\) have positive Schur property (the property, respectively) then third has well; (ii) dual \(E\) also this property; (iii) weak Dunford-Pettis property. Examples applications are provided.

Several recent papers investigated unbounded convergences in Banach lattices. The focus of this paper is to apply the results convergence classical lattice theory from a new perspective. Combining all convergences, including order (norm, absolute weak, weak*) convergence, we characterize L-weakly compact sets, operators and M-weakly on For applications, introduce so-called statistical-unbounded...

Let Bc denote the real-valued functions continuous on the extended real line and vanishing at −∞. Let Br denote the functions that are left continuous, have a right limit at each point and vanish at −∞. Define Ac to be the space of tempered distributions that are the nth distributional derivative of a unique function in Bc. Similarly with A n r from Br. A type of integral is defined on distribu...

In this paper, we generalize the concept of unbounded norm (un) convergence: let X be a normed lattice and Y a vector lattice such that X is an order dense ideal in Y ; we say that a net (yα) un-converges to y in Y with respect to X if ∥∥|yα−y|∧x∥∥→ 0 for every x ∈ X+. We extend several known results about unconvergence and un-topology to this new setting. We consider the special case when Y is...

let a be a banach algebra and e be a banach a-bimodule then s = a  e, the l1-direct sum of a and e becomes a module extension banach algebra when equipped with the algebras product (a; x):(a′; x′) = (aa′; a:x′ + x:a′). in this paper, we investigate △-amenability for these banach algebras and we show that for discrete inverse semigroup s with the set of idempotents es, the module extension bana...