Following Davie’s example of a Banach space failing the approximation property ([D]), we show how to construct a Banach space E which is asymptotically Hilbertian and fails the approximation property. Moreover, the space E is shown to be a subspace of a space with an unconditional basis which is “almost” a weak Hilbert space and which can be written as the direct sum of two subspaces all of who...

In this article, we derive computational bases for Raviart-Thomas (RT ) and Brezzi-DouglasMarini (BDM) (vector) approximation spaces on a triangulation of a domain in IR. The basis functions, defined on the reference triangle, have a Lagrangian property. The continuity of the normal component of the approximation across the edges in the triangulation is satisfied by the use of the Piola transfo...

n this paper, we consider continuity properties(especially, regularity, also viewed as an approximation property) for $%mathcal{P}_{0}(X)$-valued set multifunctions ($X$ being a linear,topological space), in order to obtain Egoroff and Lusin type theorems forset multifunctions in the Vietoris hypertopology. Some mathematicalapplications are established and several physical implications of thema...

Given a Banach space X and a subspace Y , the pair (X,Y ) is said to have the approximation property (AP) provided there is a net of finite rank bounded linear operators on X all of which leave the subspace Y invariant such that the net converges uniformly on compact subsets of X to the identity operator. The main result is an easy to apply dual formulation of this property. Applications are gi...

Abstract We establish new results on the ‐approximation property for Banach operator ideal of unconditionally p ‐compact operators in case . As a consequence our results, we provide negative answer problem posed by Kim. Namely, implies neither nor (classical) approximation property; and property. Here, denotes Sinha Karn also show all that there is closed subspace fails

We firstly give out the formulas for calculating the upper and lower approximation strict left (right)-conjunctive left (right) semi-uninorms of a binary operation. Then, we lay bare the formulas for calculating the upper and lower approximation implications, which satisfy the order property, of a binary operation. Finally, we reveal the relationships between the upper approximation strict left...

SINCE the appearance of Enflo's negative solution to the approximation problem [3], only a few positive general results on the approximation properties have been obtained. However, it is shown in [2] that any separable Banach space with the metric approximation property (M.A.P.) has the commuting metric approximation property. More precisely, if X has (MAP) there exists a sequence {Rn} of finit...