The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

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

Similarity:

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

Similarity:

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

Similarity:

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.