Displaying similar documents to “Characterizations of completeness of normed spaces through weakly unconditionally Cauchy series”

Weak Cauchy sequences in L ∞ ( μ , X )

Georg Schlüchtermann (1995)

Studia Mathematica

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For a finite and positive measure space Ω,∑,μ characterizations of weak Cauchy sequences in L ∞ ( μ , X ) , the space of μ-essentially bounded vector-valued functions f:Ω → X, are presented. The fine distinction between Asplund and conditionally weakly compact subsets of L ∞ ( μ , X ) is discussed.

Weakly precompact subsets of L₁(μ,X)

Ioana Ghenciu (2012)

Colloquium Mathematicae

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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 g ₙ ∈ c o f i : i ≥ n for each n such that for a.e. ω ∈ Ω, the sequence (gₙ(ω)) is weakly...

Some permanence results of properties of Banach spaces

Giovanni Emmanuele (2004)

Commentationes Mathematicae Universitatis Carolinae

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Using some known lifting theorems we present three-space property type and permanence results; some of them seem to be new, whereas other are improvements of known facts.