We show convergence of the weak dual greedy algorithm in wide class of Banach spaces, extending our previous result where it was shown to converge in subspaces of quotients of Lp (for 1 < p < ∞). In particular, we show it converges in the Schatten ideals Sp when 1 < p < ∞ and in any Banach lattice which is p-convex and q-concave with constants one, where 1 < p < q < ∞. We also discuss convergen...

The concept of weakorthogonality for a Banach lattice is examined. A proof that in such a lattice non expansive self maps of a non empty weakly compact convex set have fixed points is outlined. A geometric generalization of weakorthogonality is introduced and related to the Opial condition. AMS subject classification: 47H10

Let F be the set of all fuzzy numbers. In this study, we embed F into a nonseparable and non-reflexive unital Banach algebra A containing F by means of a norm defined on A, which enable us to consider F as a subset of A. Besides, the Banach lattice structure of the space A according to a partial order, we define on A has been touched on.

We consider the problem of decomposing a Banach lattice Z as a direct sum Z = X @ Y where X and Y are complemented subspaces satisfying a condition of incomparability (e.g. every operator from Y to X is strictly singular). We treat both the atomic and nonatomic cases. In particular we answer a question of Wojtaszczyk by showing that L1 fflL2 has unique structure as a nonatomic Banach lattice. O...

In this paper, we introduce the class of demi-order norm continuous operators on a Banach lattice. We study relationship between order-to-norm and operators. also investigate some properties operators, it is given characterization lattice with order by term

We discuss conditions such that strong stability and strong asymptotic compactness of a (discrete or continuous) semiflow defined on a subset in the positive cone of an ordered Banach space is preserved under asymptotic domination. This is used to show that on a Banach lattice with order continuous norm strong stability and almost periodicity of a (discrete or strongly continuous) semigroup of ...

In this paper we studyC0-semigroups onX×Lp(−h, 0;X) associated with linear differential equations with delay, whereX is a Banach space. In the case thatX is a Banach lattice with order continuous norm, we describe the associated modulus semigroup, under minimal assumptions on the delay operator. Moreover, we present a new class of delay operators for which the delay equation is well-posed for p...

A Banach space X has the complete continuity property (CCP) if each bounded linear operator from L1 into X is completely continuous (i.e., maps weakly convergent sequences to norm convergent sequences). The main theorem shows that a Banach space failing the CCP has a subspace with a nite dimensional decomposition which fails the CCP. If furthermore the space has some nice local structure (such ...

A type of Strassen's Theorem for measures taking values in the positive cone of a Banach lattice is proved. An application is given to metrics for convergence of vector measures. 1. Preliminaries: vector measures Let y be a field of subsets of a set X, and let (B, || • ||) be a Banach space. (All vector spaces we consider are assumed to have real scalars.) Then a(Sr, B) is the set of all additi...