We study Banach spaces with a weak stable unit ball, that is, where every convex combination of relatively weakly open subsets in its ball is again subset ball. It proved the class L1 preduals agree those which are purely atomic, ℓ1(Γ) for some set Γ, getting this way complete geometrical characterization atomic L1, answers setting problem. As consequence, we prove equivalence different propert...

The paper is concerned with compact bilinear operators on asymmetric normed spaces. study of multilinear spaces was initiated by Latreche and Dahia (2020) [24]. We go further in this direction prove a Schauder type theorem the compactness adjoint operator ideal properties operators. These extend some results Ramanujan Schock (1985) [34], Ruch (1989) [36], Banach On space forms one introduces an...

In a perforated domain, we consider the two-dimensional system of Navier–Stokes equations with rapidly oscillating terms in and boundary conditions. We prove that trajectory attractors this converge some weak topology to homogenized an additional potential.

A topology on a lattice L or more generally on a partially ordered set P is called an intrinsic topology if it is de ned directly from the order Early ex amples of such topologies were the interval topology of O Frink Fr and the order topology introduced by G Birkho Bi The early intrinsic topolo gies were typically symmetric i e the topology de ned on L agreed with the topology de ned on L the ...

A weak metric on a set is a function that satisfies the axioms of a metric except the symmetry and the separation axioms. The aim of this paper is to present some interesting weak metrics and to study some of their properties. In particular, we introduce a weak metric, called the Apollonian weak metric, on any subset of a Euclidean space which is either bounded or whose boundary is unbounded. W...

In view of the possibility that the 3D Navier-Stokes equations (NSE) might not always have regular solutions, we introduce an abstract framework for studying the asymptotic behavior of multi-valued dissipative evolutionary systems with respect to two topologies—weak and strong. Each such system possesses a global attractor in the weak topology, but not necessarily in the strong. In case the lat...

In this paper we discuss how to define an appropriate notion of weak topology in the Wasserstein space $(\mathcal{P}_2(\mathsf{H}),W_2)$ Borel probability measures with finite quadratic moment on a separable Hilbert $\mathsf{H}$.