Search results for "Absolute"
showing 10 items of 518 documents
Absolutely continuous functions with values in a Banach space
2017
Abstract Let Ω be an open subset of R n , n > 1 , and let X be a Banach space. We prove that α-absolutely continuous functions f : Ω → X are continuous and differentiable (in some sense) almost everywhere in Ω.
A remark on absolutely continuous functions in ℝ n
2006
We introduce the notion ofα, λ-absolute continuity for functions of several variables and we compare it with the Hencl’s definition. We obtain that eachα, λ-absolutely continuous function isn, λ-absolutely continuous in the sense of Hencl and hence is continuous, differentiable almost everywhere and satisfies change of variables results based on a coarea formula and an area formula.
On the existence of conditionally invariant probability measures in dynamical systems
2000
Let T : X→X be a measurable map defined on a Polish space X and let Y be a non-trivial subset of X. We give conditions ensuring the existence of conditionally invariant probability measures to non-absorption in Y. For dynamics which are non-singular with respect to some fixed probability measure we supply sufficient conditions for the existence of absolutely continuous conditionally invariant measures. These conditions are satisfied for a wide class of dynamical systems including systems that are Φ-mixing and Gibbs.
Absolute continuity for Banach space valued mappings
2007
We consider the notion of p,λ,δ-absolute continuity for Banach space valued mappings introduced in [2] for real valued functions and for λ = 1. We investigate the validity of some basic properties that are shared by n, λ-absolutely continuous functions in the sense of Maly and Hencl. We introduce the class $δ-BV^p_{λ,loc}$ and we give a characterization of the functions belonging to this class.
Absolutely Convergent Extensions of Nonclosable Positive Linear Functionals
2010
The existence of extensions of a positive linear functional ω defined on a dense *-subalgebra \({\mathfrak{A}_0}\) of a topological *-algebra \({\mathfrak{A}}\), satisfying certain regularity conditions, is examined. The main interest is focused on the case where ω is nonclosable and sufficient conditions for the existence of an absolutely convergent extension of ω are given.
On set-valued cone absolutely summing maps
2009
Spaces of cone absolutely summing maps are generalizations of Bochner spaces Lp(μ, Y), where (Ω, Σ, μ) is some measure space, 1 ≤ p ≤ ∞ and Y is a Banach space. The Hiai-Umegaki space \( \mathcal{L}^1 \left[ {\sum ,cbf(X)} \right] \) of integrably bounded functions F: Ω → cbf(X), where the latter denotes the set of all convex bounded closed subsets of a separable Banach space X, is a set-valued analogue of L1(μ, X). The aim of this work is to introduce set-valued cone absolutely summing maps as a generalization of \( \mathcal{L}^1 \left[ {\sum ,cbf(X)} \right] \) , and to derive necessary and sufficient conditions for a set-valued map to be such a set-valued cone absolutely summing map. We …
Factorization of absolutely continuous polynomials
2013
In this paper we study the ideal of dominated (p,s)-continuous polynomials, that extend the nowadays well known ideal of p-dominated polynomials to the more general setting of the interpolated ideals of polynomials. We give the polynomial version of Pietsch s factorization Theorem for this new ideal. Our factorization theorem requires new techniques inspired in the theory of Banach lattices.
A unified Pietsch domination theorem
2008
In this paper we prove an abstract version of Pietsch's domination theorem which unify a number of known Pietsch-type domination theorems for classes of mappings that generalize the ideal of absolutely p-summing linear operators. A final result shows that Pietsch-type dominations are totally free from algebraic conditions, such as linearity, multilinearity, etc.
Summability and estimates for polynomials and multilinear mappings
2008
Abstract In this paper we extend and generalize several known estimates for homogeneous polynomials and multilinear mappings on Banach spaces. Applying the theory of absolutely summing nonlinear mappings, we prove that estimates which are known for mappings on l p spaces in fact hold true for mappings on arbitrary Banach spaces.
On the equivalence of McShane and Pettis integrability in non-separable Banach spaces
2009
Abstract We show that McShane and Pettis integrability coincide for functions f : [ 0 , 1 ] → L 1 ( μ ) , where μ is any finite measure. On the other hand, assuming the Continuum Hypothesis, we prove that there exist a weakly Lindelof determined Banach space X, a scalarly null (hence Pettis integrable) function h : [ 0 , 1 ] → X and an absolutely summing operator u from X to another Banach space Y such that the composition u ○ h : [ 0 , 1 ] → Y is not Bochner integrable; in particular, h is not McShane integrable.