The problem and degrees of non-reflexivity
The problem and degrees of non-reflexivity (II)
The L1 Structure of Weak L1.
The Laplace transform of measures on the cone of a vector lattice.
The lattice copies of in Banach lattices
It is known that a Banach lattice with order continuous norm contains a copy of if and only if it contains a lattice copy of . The purpose of this note is to present a more direct proof of this useful fact, which extends a similar theorem due to R.C. James for Banach spaces with unconditional bases, and complements the - and -cases considered by Lozanovskii, Mekler and Meyer-Nieberg.
The lattice-almost isometric copies of and in Banach lattices.
The lattice-isometric copies of in quotients of Banach lattices.
The Levi problem for domains spread over locally convex spaces with a finite dimensional Schauder decomposition
It is proved that the Levi problem for certain locally convex Hausdorff spaces over with a finite dimensional Schauder decomposition (for example for Fréchet or Silva spaces with a Schauder basis) the Levi problem has a solution, i.e. every pseudoconvex domain spread over is a domain of existence of an analytic function. It is also shown that a pseudoconvex domain spread over a Fréchet space or a Silva space with a finite dimensional Schauder decomposition is holomorphically convex and satisfies...
The Lévy laplacian and differential operators of 2-nd order in Hilbert spaces
We shall show that every differential operator of 2-nd order in a real separable Hilbert space can be decomposed into a regular and an irregular operator. Then we shall characterize irregular operators and differential operators satisfying the maximum principle. Results obtained for the Lévy laplacian in [3] will be generalized for irregular differential operators satisfying the maximum principle.
The Lindelöf property in Banach spaces
A topological space (T,τ) is said to be fragmented by a metric d on T if each non-empty subset of T has non-empty relatively open subsets of arbitrarily small d-diameter. The basic theorem of the present paper is the following. Let (M,ϱ) be a metric space with ϱ bounded and let D be an arbitrary index set. Then for a compact subset K of the product space the following four conditions are equivalent: (i) K is fragmented by , where, for each S ⊂ D, . (ii) For each countable subset A of D, is...
The Lizorkin-Freitag formula for several weighted spaces and vector-valued interpolation
A complete description of the real interpolation space is given. An interesting feature of the result is that the whole measure space (Ω,μ) can be divided into disjoint pieces (i ∈ I) such that L is an sum of the restrictions of L to , and L on each is a result of interpolation of just two weighted spaces. The proof is based on a generalization of some recent results of the first two authors concerning real interpolation of vector-valued spaces.
The locally uniform nonsquare in generalized Cesàro sequence spaces.
The Lorentz Sequence Spaces d(w, p) Where w is Increasing.
The mapping in normed linear spaces with applications to inequalities in analysis.
The Maurey extension property for Banach spaces with the Gordon-Lewis property and related structures
The main result of this paper states that if a Banach space X has the property that every bounded operator from an arbitrary subspace of X into an arbitrary Banach space of cotype 2 extends to a bounded operator on X, then every operator from X to an L₁-space factors through a Hilbert space, or equivalently . If in addition X has the Gaussian average property, then it is of type 2. This implies that the same conclusion holds if X has the Gordon-Lewis property (in particular X could be a Banach...
The maximum distance between two-dimensional Banach spaces.
The maximum path theorem and extreme points of James space
The Mazur intersection property for families of closed bounded convex sets in Banach spaces
The Menelaus Property characterizes real rotund Banach spaces
The minimal displacement problem in subspaces of the space of continuous functions of finite codimension
We show that every subspace of finite codimension of the space C[0,1] is extremal with respect to the minimal displacement problem.