Narcisse Randrianantoanina, Elias Saab
Let $X$ be a Banach space $E$ a Köthe function space that does not contain $c_0$. It is shown that the vector valued function space $E(X)$ has the Near Radon Nikodym property if and only if $X$ does.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
We give necessary and sufficient conditions for a Banach space $X$ having the Radon-Nikodým property in terms of polynomial spline sequences.
The aim of this note is to establish two Radon--Nikodym type theorems for nonnegative Hermitian forms defined on a real or complex vector space. We apply these results to prove the known Radon--Nikodym theorems of the theory of representable positive functionals, $σ$-additive and finitely additive measures.
Let X be a separable Banach space and Y a space which has the Radon-Nikodym property. In this work, we show that L(X, Y) has the Radon-Nikodym property, if L(X, Y) is weakly locally uniformly convex or if L(X, Y) is a weakly compactly gen- erated space.
It is well known that every bounded below and non increasing sequence in the real line converges. We give a version of this result valid in Banach spaces with the Radon-Nikodym property, thus extending a former result of A. Procházka.
A small Radon-Nikodým compact space from a parametrized diamond
本文在参数化钻石原则下构造了一个权为 $\aleph_1$ 的 Radon-Nikodým 紧空间，并证明其连续像不再是 Radon-Nikodým 空间，部分回答了已有文献中的公开问题。
A Radon-Nikodym theorem for monotone measures
本文针对单调测度上的Choquet积分证明了Radon-Nikodym定理，给出有限单调测度对具有Radon-Nikodym性质的充要条件，并将结果推广到σ-有限单调测度情形。
We extend the well-known criterion of Lotz for the dual Radon-Nikodym property (RNP) of Banach lattices to finitely generated Banach $C(K)$-modules and Banach $C(K)$-modules of finite multiplicity. Namely, we prove that if $X$ is a Banach space from one of these classes then its Banach dual $X^\star$ has the RNP iff $X$ does not contain a closed subspace isomorphic to $\ell^1$.
Some topics concerning the Gould integral are presented here: new results of integrability on finite measure spaces with values in an M-space are given, together with a Radon-Nikodym theorem relative to a Gould-type integral of real functions with respect to a multisubmeasure.
Given an Orlicz $N$-function $φ$ and a positive decreasing weight $w$, we present criteria of the diameter two property and of the Radon-Nikodým property in Orlicz-Lorentz function and sequence spaces $Λ_{φ,w}$ and $λ_{φ,w}$. We show that in the spaces $Λ_{φ,w}$ or $λ_{φ,w}$ equipped with the Luxemburg norm, the diameter of any relatively weakly subset of the unit ball in these spaces is two if and only if $φ$ does not satisfy the appropriate $Δ_2$ condition, while they have the Radon-Nikodým property if and only if $φ$ satisfies the appropriate $Δ_2$ condition.
Admissible vectors lead to frames or coherent states under the action of a group by means of square integrable representations. This work shows that admissible vectors can be seen as weights with central support on the (left) group von Neumann algebra. The analysis involves spatial and cocycle derivatives, noncommutative $L^p$-Fourier transforms and Radon-Nikodym theorems. Square integrability confine the weights in the predual of the algebra and everything may be written in terms of a (right selfdual) bounded element.
Sharpness Loss for Radon--Nikodym Derivatives of Completely Positive Maps
本文研究完全正映射复合下投影值Radon--Nikodym导数的尖锐性保持问题，证明尖锐性损失由拉回映射的乘法缺陷决定，并给出有限维情形下的判据与量化。
If $μ_1,μ_2,\dots$ are positive measures on a measurable space $(X,Σ)$ and $v_1,v_2, \dots$ are elements of a Banach space ${\mathbb E}$ such that $\sum_{n=1}^\infty \|v_n\| μ_n(X) < \infty$, then $ω(S)= \sum_{n=1}^\infty v_n μ_n(S)$ defines a vector measure of bounded variation on $(X,Σ)$. We show ${\mathbb E}$ has the Radon-Nikodym property if and only if every ${\mathbb E}$-valued measure of bounded variation on $(X,Σ)$ is of this form. As an application of this result we show that under natural conditions an operator defined on positive measures, has a unique extension to an operator defin…
We present a natural and simple proof of the Radon - Nikodym theorem for measures with values in the space of bounded linear operators on a separable Hilbert space. This space is not separable, that is why it is essential to assume in the theorem that the range of the measure is separable. We also discuss distinctions between uniform and strong operator measures (Remark 3.3 to Lemma 3.2, Theorem 3.5 and its Corollary 3.6). Proof of this version of the Radon - Nikodym theorem either is not presented in known literature, or given for special cases and with some inaccuracies (see Comment at the e…
A compact space is said to be weakly Radon-Nikodým if it is homeomorphic to a weak*-compact subset of the dual of a Banach space not containing an isomorphic copy of $\ell_1$. In this work we provide an example of a continuous image of a Radon-Nikodým compact space which is not weakly Radon-Nikodým. Moreover, we define a superclass of the continuous images of weakly Radon-Nikodým compact spaces and study its relation with Corson compacta and weakly Radon-Nikodým compacta.
We construct a continuous image of a Radon-Nikodým compact space which is not Radon-Nikodým compact, solving the problem posed in the 80ties by Isaac Namioka.
For a pair of bounded linear Hilbert space operators $A$ and $B$ one considers the Lebesgue type decompositions of $B$ with respect to $A$ into an almost dominated part and a singular part, analogous to the Lebesgue decomposition for a pair of measures (in which case one speaks of an absolutely continuous and a singular part). A complete parametrization of all Lebesgue type decompositions will be given, and the uniqueness of such decompositions will be characterized. In addition, it will be shown that the almost dominated part of $B$ in a Lebesgue type decomposition has an abstract Radon-Nikod…
A compact space is said to be weakly Radon-Nikodým (WRN) if it can be weak*-embedded into the dual of a Banach space not containing $\ell_1$. We investigate WRN Boolean algebras, i.e. algebras whose Stone space is WRN compact. We show that the class of WRN algebras and the class of minimally generated algebras are incomparable. In particular, we construct a minimally generated nonWRN Boolean algebra whose Stone space is a separable Rosenthal compactum, answering in this way a question of W. Marciszewski. We also study questions of J. Rodríguez and R. Haydon concerning measures and the existenc…
Group equivariant Radon-Nikodým property and its characterizations
研究巴拿赫空间在群作用下的等变拉东 - 尼科迪姆性质等相关概念，利用抽象调和分析和表示理论工具，建立了紧致群和局部紧致且第二可数群作用下这些性质对应物之间的蕴含关系及等价关系。
We introduce the symmetric-Radon-Nikodým property (sRN property) for finitely generated s-tensor norms $β$ of order $n$ and prove a Lewis type theorem for s-tensor norms with this property. As a consequence, if $β$ is a projective s-tensor norm with the sRN property, then for every Asplund space $E$, the canonical map $\widetilde{\otimes}_β^{n,s} E' \to \Big(\widetilde{\otimes}_{β'}^{n,s} E \Big)'$ is a metric surjection. This can be rephrased as the isometric isomorphism $\mathcal{Q}^{min}(E) = \mathcal{Q}(E)$ for certain polynomial ideal $\Q$. We also relate the sRN property of an s-tensor n…
In this paper we define the Radon-Nikodym class (RN class) of locally convex topological vector spaces. The RN class is characterized in terms of the Radon-Nikodym theorem for vector measures using integrable by seminorm derivatives. It is shown that the RNP class of all complete Hausdorff locally convex spaces possessing the Radon-Nikodym property is properly contained in the RN class. As an application we present a Radon-Nikodym theorem for multimeasures with respect to the Pettis integrable multifunctions in terms of the RN class.
We clarify the relation between inverse systems, the Radon-Nikodym property, the Asymptotic Norming Property of James-Ho, and the GFDA spaces introduced in our earlier paper on differentiability of Lipschitz maps into Banach spaces.
Some necessary and sufficient conditions are found for Banach function lattices to have the Radon-Nikodým property. Consequently it is shown that an Orlicz space $L_φ$ over a non-atomic $σ$-finite measure space $(Ω, Σ,μ)$, not necessarily separable, has the Radon-Nikodým property if and only if $φ$ is an $N$-function at infinity and satisfies the appropriate $Δ_2$ condition. For an Orlicz sequence space $\ell_φ$, it has the Radon-Nikodým property if and only if $φ$ satisfies condition $Δ_2^0$. In the second part the relationships between uniformly $\ell_1^2$ points of the unit sphere of a Bana…
We prove that a continuous image of a Radon-Nikodým compact space of weight less than b is Radon-Nikodým compact. As a Banach space counterpart, subspaces of Asplund generated Banach spaces of density character less than b are Asplund generated. In this case, in addition, there exists a subspace of an Asplund generated space which is not Asplund generated which has density character exactly b.
We study dentable maps from a closed convex subset of a Banach space into a metric space as an attempt of generalize the Radon-Nikodým property to a "less linear" frame. We note that a certain part of the theory can be developed in rather great generality. Indeed, we establish that the elements of the dual which are "strongly slicing" for a given uniformly continuous dentable function form a dense $\mathcal{G}_δ$ subset of the dual. As a consequence, the space of uniformly continuous dentable maps from a closed convex bounded set to a Banach space is a Banach space. However some interesting ap…
We prove a Rademacher-type theorem for Lipschitz mappings from a subset of a Carnot group to a Banach homogeneous group, equipped with a suitably weakened Radon-Nikodym property. We provide a metric area formula that applies to these mappings and more generally to all almost everywhere metrically differentiable Lipschitz mappings defined on a Carnot group.
We show that a geodesic metric space which does not admit bilipschitz embeddings into Banach spaces with the Radon-Nikodým property does not necessarily contain a bilipschitz image of a thick family of geodesics. This is done by showing that any thick family of geodesics is not Markov convex, and comparing this result with results of Cheeger-Kleiner, Lee-Naor, and Li. The result contrasts with the earlier result of the author that any Banach space without the Radon-Nikodým property contains a bilipschitz image of a thick family of geodesics.
A brief review of Radon-Nikodýmification
本文回顾了抽象测度空间的Radon-Nikodýmification近期研究成果，包括积分几何测度的特例及其在SBV对偶中的应用。
Idempotent integration is an analogue of the Lebesgue integration where $σ$-additive measures are replaced by $σ$-maxitive measures. It has proved useful in many areas of mathematics such as fuzzy set theory, optimization, idempotent analysis, large deviation theory, or extreme value theory. Existence of Radon--Nikodym derivatives, which turns out to be crucial in all of these applications, was proved by Sugeno and Murofushi. Here we show a converse statement to this idempotent version of the Radon--Nikodym theorem, i.e. we characterize the $σ$-maxitive measures that have the Radon--Nikodym pr…
Wasserstein spaces have the Radon-Nikodym property
本文证明Wasserstein空间在垂直与水平两种几何下均具有Radon-Nikodym性质，并由此推导变分原理、向量测度定理及鞅收敛结果，同时引入水平鞅并刻画其为L^p值鞅的分布。
In this paper, we introduce the concept of completely positive matrix of linear maps on Hilbert $A$-modules over locally $C^{*}$-algebras and prove an analogue of Stinespring theorem for it. We show that any two minimal Stinespring representations for such matrices are unitarily equivalent. Finally, we prove an analogue of the Radon--Nikodym theorem for this type of completely positive $n\times n$ matrices.
Johnson and Schechtman (2009) characterized superreflexivity in terms of finite diamond graphs. The present author characterized the Radon-Nikodým property (RNP) for dual spaces in terms of the infinite diamond. This paper is devoted to further study of relations between metric characterizations of superreflexivity and the RNP for dual spaces. The main result is that finite subsets of any set $M$ whose embeddability characterizes the RNP for dual spaces, characterize superreflexivity. It is also observed that the converse statement does not hold, and that $M=\ell_2$ is a counterexample.
We characterize Banach spaces with polynomial numerical index 1 when they have the Radon-Nikodým property. The holomorphic numerical index is introduced and the characterization of the Banach space with holomorphic numerical index 1 is obtained when it has the Radon-Nikodým property.
We prove the differentiability of Lipschitz maps X-->V, where X is a complete metric measure space satisfying a doubling condition and a Poincaré inequality, and V is a Banach space with the Radon Nikodym Property (RNP). The proof depends on a new characterization of the differentiable structure on such metric measure spaces, in terms of directional derivatives in the direction of tangent vectors to suitable rectifiable curves.
The Radon-Nikod$\acute{Y}$m property of $\mathbb{L}$-Banach spaces and the dual representation theorem of $\mathbb{L}$-Bochner function spaces
本文定义有限测度空间上的 $\mathbb{L}$-Bochner 可积函数，研究其完备性与 $\mathbb{L}$-Banach 空间的 RNP，并给出反例及对偶表示定理。
We show that an operator valued $α$-completely positive map on a group G is given by a unitary representation of G on a Krein space which satisfies some condition. Moreover, two unitary equivalent such unitary representations define the same α-completely positive map. Also we introduce a pre-order relation on the collection of α-completely positive maps on a group and we characterize this relation in terms of the unitary representation associated to each map.
We find a class of metric structures which do not admit bilipschitz embeddings into Banach spaces with the Radon-Nikodým property. Our proof relies on Chatterji's (1968) martingale characterization of the RNP and does not use the Cheeger's (1999) metric differentiation theory. The class includes the infinite diamond and both Laakso (2000) spaces. We also show that for each of these structures there is a non-RNP Banach space which does not admit its bilipschitz embedding. We prove that a dual Banach space does not have the RNP if and only if it admits a bilipschitz embedding of the infinite dia…
Kernel Radon-Nikodym Derivatives for Random Matrix Products
本文研究了随机矩阵乘积关联的时间索引正定核的一步移位的核Radon-Nikodym导数，探讨了移位核被原核支配的条件及对应的Radon-Nikodym导数，通过非均匀方差和高斯Kraus乘积两种模型进行分析。
In this paper we present a generalization of the Radon-Nikodym theorem proved by Pedersen and Takesaki. Given a normal, semifinite and faithful (n.s.f.) weight $ϕ$ on a von Neumann algebra M and a strictly positive operator $δ$, affiliated with M and satisfying a certain relative invariance property with respect to the modular automorphism group $σ^ϕ$ of $ϕ$, with a strictly positive operator as the invariance factor, we construct the n.s.f. weight $ϕ(δ^{1/2} . δ^{1/2})$. All the n.s.f. weights on M whose modular automorphisms commute with $σ^ϕ$ are of this form, the invariance factor being af…
Banach spaces without the Radon-Nikodým property are characterized as spaces containing bilipschitz images of thick families of geodesics defined as follows. A family $T$ of geodesics joining points $u$ and $v$ in a metric space is called {\it thick} if there is $α>0$ such that for every $g\in T$ and for any finite collection of points $r_1,...,r_n$ in the image of $g$, there is another $uv$-geodesic $\widetilde g\in T$ satisfying the conditions: $\widetilde g$ also passes through $r_1,...,r_n$, and, possibly, has some more common points with $g$. On the other hand, there is a finite collectio…
The order relation on the set of completely n-positive linear maps from a pro-C*-algebra A to L(H), the C*-algebra of bounded linear operators on a Hilbert space H, is characterized in terms of the representation associated with each completely n-positive linear map. Also, the pure elements in the set of all completely n-positive linear maps from A to L(H) and the extreme points in the set of unital completely n-positive linear maps from A to L(H) are characterized in terms of the representation induced by each completely n-positive linear map.
We prove that every Banach space, not necessarily separable, can be isometrically embedded into a $\mathcal L_{\infty}$-space in a way that the corresponding quotient has the Radon-Nikodym and the Schur properties. As a consequence, we obtain $\mathcal L_\infty$ spaces of arbitrary large densities with the Schur and the Radon-Nikodym properties. This extents the a classical result by J. Bourgain and G. Pisier.
052<p type="texpara" tag="Body Text" et="abstract" >A completely $n$ -positive linear map from a locally $C^{\ast}$-algebra $A$ to another locally $C^{\ast}$-algebra $B $is an $n\times n$ matrix whose elements are continuous linear maps from $A$ to $B$ and which verifies the condition of completely positivity. In this paper we prove a Radon-Nikodym type theorem for strict completely $n$-positive linear maps which describes the order relation on the set of all strict completely $n$ -positive linear maps from a locally $C^{\ast }$-algebra $A$ to a $C^{\ast}$-algebra $B$, in terms of a self-dual …
A categorical treatment of the Radon-Nikodym theorem and martingales
本文用范畴论方法证明Radon-Nikodym定理，通过自然同构与Kan延拓推广至一般概率空间，并利用右Kan延拓中的条件期望范畴化表示鞅，进而在丰富范畴中证明鞅收敛定理。
$L^p$-Integrability of Radon-Nikodym Densities Between Harmonic Energy Measures on the Sierpinski Gasket
研究谢尔宾斯基垫片上非常数调和函数能量测度间拉东 - 尼科迪姆密度的$L^p$可积性，通过证明密度比幂和一致有界，得出在特定子区间及特定条件下的$L^p$可积性结论。
Let $Σ$ be a $σ$-algebra over $Ω$, and let $M(Σ)$ denote the Banach space of complex measures. Consider a representation $T_t$ for $t\in\Bbb R$ acting on $M(Σ)$. We show that under certain, very weak hypotheses, that if for a given $μ\in M(Σ)$ and all $A \in Σ$ the map $t \mapsto T_t μ(A)$ is in $H^\infty(\Bbb R)$, then it follows that the map $t \mapsto T_t μ$ is Bochner measurable. The proof is based upon the idea of the Analytic Radon Nikodým Property. Straightforward applications yield a new and simpler proof of Forelli's main result concerning analytic measures ({\it Analytic and quasi-in…
We study when the integration maps of vector measures can be computed as pointwise limits of their finite rank Radon-Nikodým derivatives. We will show that this can sometimes be done, but there are also principal cases in which this cannot be done. The positive cases are obtained using the circle of ideas of the approximation property for Banach spaces. The negative ones are given by means of an adequate use of the Daugavet property. As an application, we analyse when the norm in a space of integrable functions $L^1(m)$ can be computed as a limit of the norms of the spaces of integrable functi…
Russo-Dye type Theorem, Stinespring representation,and Radon Nikodym dervative for invariant block multilinear completely positive maps
本文研究了不变多重线性完全正映射的性质，证明了其 Russo-Dye 型定理、自动对称性与完全有界性，引入了不变块 CP 映射的多重线性版本，推导出极小 Stinespring 膨胀并获得了 Radon Nikodym 定理。
A Bochner-type integration theory for random normed modules
本文发展了随机范数模的测度与积分理论，研究了值域为L^0(m)的测度，并建立了针对完整随机范数模的Bochner型积分理论，证明了Radon-Nikodým定理和Riesz-Markov-Kakutani表示定理的版本，并探讨了其应用。
We construct the generalized Lebesgue--Bochner spaces $L^p(μ,\varPi)$ for positive measures $μ$ and for suitable real or complex topological vector spaces $\varPi$ so that for $1<p<+\infty$ and Banachable $\varPi$ with separable topology the strong dual of the classical Bochner space $L^p(μ,\varPi)$ becomes canonically represented by $L^{p^*}(μ,\varPi_σ')\,$. Hence we need no separability assumption of the norm topology of the strong dual $\varPi_β'$ of $\varPi$. For $p=1$ and for suitably restricted positive measures $μ$ we even get a similar result without any separability of the norm topolo…
Approximations of Lipschitz maps with maximal derivatives on Banach spaces
本文研究Banach空间上Lipschitz映射的两类逼近，用强范数可达和最大导数可达映射刻画Radon-Nikodým性质，并证明实直线上Lipschitz泛函可被最大仿射函数局部逼近但无法一致逼近。
The possibility of getting a Radon-Nikodym type theorem and a Lebesgue-like decomposition for a non necessarily positive sesquilinear $Ω$ form defined on a vector space $\mathcal D$, with respect to a given positive form $Θ$ defined on $\D$, is explored. The main result consists in showing that a sesquilinear form $Ω$ is $Θ$-regular, in the sense that it has a Radon-Nikodym type representation, if and only if it satisfies a sort Cauchy-Schwarz inequality whose right hand side is implemented by a positive sesquilinear form which is $Θ$-absolutely continuous. In the particular case where $Θ$ is …
Banach-valued graph limits: Graphon representability and Banach-space structure
该研究关联带巴拿赫装饰的图的图极限问题与巴拿赫空间结构，揭示了不同类型巴拿赫空间满足对应图子表示性质的充要条件。
On weak convergence in Köthe-Bochner function spaces
研究Köthe-Bochner函数空间中弱收敛的性质，证明当X*不满足Radon-Nikodým性质时，存在一个有界非弱零序列，使其与E*(X*)中所有元素的配对趋于零，从而推翻了James边界的相关结论。
Let $X$ be a Banach space and $Γ\subseteq X^*$ a total linear subspace. We study the concept of $Γ$-integrability for $X$-valued functions $f$ defined on a complete probability space, i.e. an analogue of Pettis integrability by dealing only with the compositions $\langle x^*,f \rangle$ for $x^*\in Γ$. We show that $Γ$-integrability and Pettis integrability are equivalent whenever $X$ has Plichko's property ($\mathcal{D}'$) (meaning that every $w^*$-sequentially closed subspace of $X^*$ is $w^*$-closed). This property is enjoyed by many Banach spaces including all spaces with $w^*$-angelic dual…
We prove that if a compact line is fragmentable, then it is a Radon-Nikodým compact space.
We give a short proof of the recent results that, for every $1\leq p< \infty,$ the Ces{à}ro function space $Ces_p(I)$ is not a dual space, has the weak Banach-Saks property and does not have the Radon-Nikodym property.
We study the $H^1$-projective Banach spaces. We prove that they have the Analytic Radon-Nikodym Property, and that they are cotype 2 spaces which satisfy Grothendieck's Theorem. We show also that the ultraproduct of $H^1$-projective spaces is $H^1$-projective. Other results are also discussed.
Aubin--Lions Compactness for Stieltjes--Bochner Evolution Graphs
本文针对 Stieltjes--Bochner 演化图建立 Aubin--Lions 紧性定理，结合原子求值与局部平均，推广经典结果至混合测度情形。
Construction under Martin's axiom of a Boolean algebra with the Grothendieck property but without the Nikodym property
该研究在弱Martin公理假设下构造特殊完全不连通紧Hausdorff空间，改进了Talagrand的结果，证明Martin公理蕴含存在具Grothendieck性质但无Nikodym性质的布尔代数。
Let $A$ be a Lebesgue measure space. We interpret measures on $A\times A\times R_+$ as 'maps' from $A$ to $A$, which spread $A$ along itself; their Radon-Nikodym derivatives also are spread. We discuss basic properties of the semigroup of such maps and the action of this semigroup in the spaces $L^p(A)$.
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。