Radon-Nikodym property for vector-valued integrable functions
It is proved that if a Frechet space has property, then also has property, for .
Radon-Nikodym type properties for Banach spaces
Raising bounded groups and splitting of radical extensions of commutative Banach algebras
Let A be a commutative unital Banach algebra and let A/ℛ be the quotient algebra of A modulo its radical ℛ. This paper is concerned with raising bounded groups in A/ℛ to bounded groups in the algebra A. The results will be applied to the problem of splitting radical extensions of certain Banach algebras.
Random fixed points for a certain class of asymptotically regular mappings
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...
Random Fourier Series with Respect to a General Orthonormal System in L...(..) Spaces.
Random linear functionals and random integrals
Random matrices, amalgamated free products and subfactors of the von Neumann algebra of a free group, of noninteger index.
Random matrices and -theory for exact -algebras.
Random -normed linear space.
Random rearrangements in functional spaces.
We give an operator approach to several inequalities of S. Kwapien and C. Schütt, which allows us to obtain more general results.
Random seminormed spaces
Random trilinear forms and the Schur multiplication of tensors.
Random ε-nets and embeddings in
We show that, given an n-dimensional normed space X, a sequence of independent random vectors , uniformly distributed in the unit ball of X*, with high probability forms an ε-net for this unit ball. Thus the random linear map defined by embeds X in with at most 1 + ε norm distortion. In the case X = ℓ₂ⁿ we obtain a random 1+ε-embedding into with asymptotically best possible relation between N, n, and ε.
Randomness and pattern in convex geometric analysis.
Randverteilungen holomorpher Funktionen und die Topologie von D'.
Range inclusion results for derivations on noncommutative Banach algebras
Let A be a Banach algebra, and let D : A → A be a (possibly unbounded) derivation. We are interested in two problems concerning the range of D: 1. When does D map into the (Jacobson) radical of A? 2. If [a,Da] = 0 for some a ∈ A, is Da necessarily quasinilpotent? We prove that derivations satisfying certain polynomial identities map into the radical. As an application, we show that if [a,[a,[a,Da]]] lies in the prime radical of A for all a ∈ A, then D maps into the radical. This generalizes a result...
Range of a contractive strongly positive projection in a C*-algebra
We generalize a result of Choi and Effros on the range of a contractive completely positive projection in a C*-algebra to the case when this projection is only strongly positive using, moreover, an elementary argument instead of a 2×2-matrix technique.
Range of operators and regularity of solutions
Range of the horocyclic Radon transform on trees
In this paper we study the Radon transform on the set of horocycles of a homogeneous tree , and describe its image on various function spaces. We show that the functions of compact support on that satisfy two explicit Radon conditions constitute the image under of functions of finite support on . We extend these results to spaces of functions with suitable decay on , whose image under satisfies corresponding decay conditions and contains distributions on that are not defined pointwise....
Range tripotents and order in JBW*-triples
In a JBW*-triple, i.e., a symmetric complex Banach space possessing a predual, the set of tripotents is naturally endowed with a partial order relation. This work is mainly concerned with this partial order relation when restricted to the subset 𝓡(A) of tripotents in a JBW*-triple B formed by the range tripotents of the elements of a JB*-subtriple A of B. The aim is to present recent developments obtained for the poset 𝓡(A) of the range tripotents relative to A, whilst also providing the necessary...