Weak compactness criteria and convergences in LE1(μ).
Weak orthogonality and weak property () in some Banach sequence spaces
It is proved that a Köthe sequence space is weakly orthogonal if and only if it is order continuous. Criteria for weak property () in Orlicz sequence spaces in the case of the Luxemburg norm as well as the Orlicz norm are given.
Weak uniform continuity and weak sequential continuity of continuous n-linear mappings between Banach spaces.
In this paper it is shown that the class LnWU (E1,E2,...,En;F) of weakly uniformly continuous n-linear mappings from E1x E2x...x En to F on bounded sets coincides with the class LnWSC (E1,E2,...,En;F) of weakly sequentially continuous n-linear mappings if and only if for every Banach space F, each Banach space Ei for i = 1,2,...,n does not contain a copy of l1.
Weakly almost periodic vector-valued functions [Book]
Weakly compact composition operators on analytic vector-valued function spaces.
Weakly compact operators from a B-space into the space of Bochner integrable functions
Weakly compact operators on Köthe-Bochner spaces with the mixed topology
Let E be a Banach function space and let X be a real Banach space. We examine weakly compact linear operators from a Köthe-Bochner space E(X) endowed with some natural mixed topology (in the sense of Wiweger) to a Banach space Y.
Weakly continuous functions of Baire class 1.
For a compact Hausdorff space K and a Banach space X, let WC(K,X) denote the space of X-valued functions defined on K, that are continuous when X has the weak topology. In this note by a simple Banach space theoretic argument, we show that given f belonging to WC(K,X) there exists a net {fa} contained in C(K,X) (space of norm continuous functions) such that fa --> f pointwise w.r.t. the norm topology on X. Such a function f is said to be of Baire class 1.
Weakly precompact subsets of L₁(μ,X)
Let (Ω,Σ,μ) be a probability space, X a Banach space, and L₁(μ,X) the Banach space of Bochner integrable functions f:Ω → X. Let W = f ∈ L₁(μ,X): for a.e. ω ∈ Ω, ||f(ω)|| ≤ 1. In this paper we characterize the weakly precompact subsets of L₁(μ,X). We prove that a bounded subset A of L₁(μ,X) is weakly precompact if and only if A is uniformly integrable and for any sequence (fₙ) in A, there exists a sequence (gₙ) with for each n such that for a.e. ω ∈ Ω, the sequence (gₙ(ω)) is weakly Cauchy in X....
Weighted diffeomorphism groups of Banach spaces and weighted mapping groups [Book]
Weighted estimates for commutators of linear operators
We study boundedness properties of commutators of general linear operators with real-valued BMO functions on weighted spaces. We then derive applications to particular important operators, such as Calderón-Zygmund type operators, pseudo-differential operators, multipliers, rough singular integrals and maximal type operators.
Weighted locally convex spaces of measurable functions.
Weighted topology in the non-locally convex setting
Wiener Tauberian theorems for vector-valued functions.