The Rademacher sums are investigated in the BMO space on [0,1]. They span an uncomplemented subspace, in contrast to the dyadic space on [0,1], where they span a complemented subspace isomorphic to l₂. Moreover, structural properties of infinite-dimensional closed subspaces of the span of the Rademacher functions in BMO are studied and an analog of the Kadec-Pełczyński type alternative with l₂ and c₀ spaces is proved.
The Rademacher sums are investigated in the Cesàro spaces (1 ≤ p ≤ ∞) and in the weighted Korenblyum-Kreĭn-Levin spaces on [0,1]. They span l₂ space in for any 1 ≤ p < ∞ and in if and only if the weight w is larger than on (0,1). Moreover, the span of the Rademachers is not complemented in for any 1 ≤ p < ∞ or in for any quasi-concave weight w. In the case when p > 1 and when w is such that the span of the Rademacher functions is isomorphic to l₂, this span is a complemented...
We study the behaviour of the Rademacher functions in the weighted Cesàro spaces Ces(ω,p), for ω(x) a weight and 1 ≤ p ≤ ∞. In particular, the case when the Rademacher functions generate in Ces(ω,p) a closed linear subspace isomorphic to ℓ² is considered.
We establish weighted Hardy-Littlewood inequalities for radial derivative and fractional radial derivatives on bounded symmetric domains.
It is proved that if a Frechet space has property, then also has property, for .
Let (Ω, σ) be a measurable space and K a nonempty bounded closed convex separable subset of a p-uniformly convex Banach space E for p > 1. We prove a random fixed point theorem for a class of mappings T:Ω×K ∪ K satisfying the condition: For each x, y ∈ K, ω ∈ Ω and integer n ≥ 1, ⃦Tⁿ(ω,x) - Tⁿ(ω,y) ⃦ ≤ aₙ(ω)· ⃦x - y ⃦ + bₙ(ω) ⃦x -Tⁿ(ω,x) ⃦ + ⃦y - Tⁿ(ω,y) ⃦ + cₙ(ω) ⃦x - Tⁿ(ω,y) ⃦ + ⃦y - Tⁿ(ω,x) ⃦, where aₙ, bₙ, cₙ: Ω → [0, ∞) are functions satisfying certain conditions and Tⁿ(ω,x) is the value...
We give an operator approach to several inequalities of S. Kwapien and C. Schütt, which allows us to obtain more general results.
For 0 ≤ α < 1, an operator U ∈ L(X,Y) is called a rank α operator if implies Uxₙ → Ux in norm. We give some results on rank α operators, including an interpolation result and a characterization of rank α operators U: C(T,X) → Y in terms of their representing measures.