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1.
给出 Banach空间列{Xi}i=1∞的 lp乘积B-凸的特征刻划, 证明B-凸空间上的每个黎斯算子可West分解,即分解成一个紧算子和一个拟幂 零算子的和. 相似文献
2.
Carlo Sempi 《Mediterranean Journal of Mathematics》2006,3(2):283-300
This contribution aims at presenting a survey of a portion of the theory of Probabilistic Normed spaces. No result will be proved, so that the reader is referred to the original sources for the proofs. The theory of PN
spaces has many facets and touches on many branches of mathematics, for instance, geometry, functional analysis, topology,
probability. This justifies the adjective “partial” that appears in the title. Therefore, it is perhaps better to declare
from the start what one may expect from this survey. It is only natural to investigate which “classical”properties of normed
spaces are preserved in the new setting. But it is probably more interesting to look for those properties that pertain to
the new theory and which have no corresponding analogue in the classical theory. It must also be added that Probabilistic
Normed spaces may be approached from different standpoints: they may be studied for their own sake, as a special subject in
functional analysis or in topology that is worth investigating simply because it is there, or because it provides a tool to
approach open problems or, again, to shed light on topics that one thought had been thoroughly investigated. In this, one
thinks immediately of the possible applications in probability and statistics.
This paper was written as a part of the project “Metodi stocastici in finanza matematica” of the Italian M.I.U.R.. 相似文献
3.
Witold Wnuk 《Mathematische Nachrichten》2010,283(5):775-779
The paper is devoted to investigations of the order structure of ultrapowers. A characterization of discrete normed lattices, all of whose ultrapowers are discrete, is presented (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
4.
在实赋范空间上通过范数导数(左、右两个)引进一种广义内积(上、下两个),并用它们对实赋范空间上的线性连续泛函给出上、下估计式。本文主要结果揭示了实赋范空间上的如下三类连续线性泛函的统一性。第一类连续线性泛函是指其中每一个f都在闭单位球上取到其范数值f。第二类连续线性泛函是指其中第一个f的核Ker(f)与另一空间元素之间的最佳逼近元存在。第三类连续性泛函是指其中每一个f的上限和下限分别可用上、下两种 相似文献
5.
基于概率测度理论基础,研究了随机赋范空间中算子随机范数,得到了线性算子空间与线性泛函的若干随机化结果与随机化的Hahn-Banach延拓定理.结果可能成为随机泛函分析与概率论及应用的理论工具. 相似文献
6.
In this paper, we present various notions and aspects of orthogonality in normed spaces. Characterizations and generalizations of orthogonality are also considered. Results on orthogonality of the range and the kernel of elementary operators and the operators implementing them also are given. 相似文献
7.
In this paper, the concepts of probabilistic normed Riesz space and probabilistic Banach lattice are introduced, and their basic properties are studied. In this context, some continuity and convergence theorems are proved. 相似文献
8.
One of the best ways of studying ordered algebraic structures is through their spectra. The three well-known spectra usually considered are the Brumfiel, Keimel, and the maximal spectra. The pointfree versions of these spectra were studied by B. Banaschewski for f-rings. Here, we give the pointfree versions of the Keimel and the maximal spectra for Riesz spaces. Moreover, we briefly mention how one can use the results of this paper to give a pointfree version of the Kakutani duality for Riesz spaces. 相似文献
9.
§1. Definitions,LemmasandTheoremDefinition1[1] Let(X,y·y)bearealnormedlinearspaceofdemensiongreaterthan1,wedefineanglesAm,n(x,y)betweennonzerovectorsxandyinXbyAm,n(x,y)=cos-1nyxyxy+yyyyy2-myxyxy-yyyyy2+2(m-n)2(m+n),heremandnaretwonon-negentiveinte-ge… 相似文献
10.
11.
For a class of linear operators including Riesz potentials on R^d with a nonnegative Radon measure μ, which only satisfies some growth condition, the authors prove that their boundedness in Lebesgue spaces is equivalent to their boundedness in the Hardy space or certain weak type endpoint estimates, respectively. As an application, the authors obtain several new end estimates. 相似文献
12.
By using the discrete Calderón reproducing formulae, the author first establishes the boundedness of the Riesz-potential-type operator in homogeneous Besov and Triebel–Lizorkin spaces over spaces of homogeneous type. Then, by use of the T1 theorems for these spaces, the author proves that this operator of Riesz potential type can be used as the lifting operator of these spaces. 相似文献
13.
设{Ei:i∈I}是一族ArchmideanRiesz空间.记Πi∈IEi为Riesz乘积空间.此文的主要结论是:存在一个完全正则Housdorf空间X使得Πi∈IEiRiesz同构于C(X)的充分必要条件是对每一个i∈I存在一个完全正则Housdorf空间Xi使得EiRiesz同构于C(Xi). 相似文献
14.
主要讨论一类齐次群上限制算子的映照性质,并且应用所得结果证明这类齐次群上Riesz平均的混合范数有界性。 相似文献
16.
姚喜妍 《应用泛函分析学报》2008,10(2):155-161
引入并研究了Banach空间X中的Bessel集、广义框架与广义Riesz基.对X中的任一Bessel集{gm}m∈M,定义有界线性算子T:L^2(P)→X^*,利用算子丁,给出了Bessel集与广义框架的等价刻画.同时讨论了广义框架和广义Riesz基的摄动. 相似文献
17.
本文研究了紧致齐性空间上的Riesz位势算子与Bessel位势算子,Riesz变换与Bessel变换,给出了上述算子对应的核函数的具体构造并证明了Riesz变换与Bessel变换作为奇异积分算子的H ̄p有界性,p>0。 相似文献
18.
We obtain some expressions for the Riesz angles of Orlicz sequence spaces endowed with the Luxemburg and Orlicz norms and show some practical ways of computation. 相似文献
19.
In this paper, the authors give a characterization of the (L
p, λ
, L
q, λ
)-compactness for the Riesz potential commutator [b,I
α
]. More precisely, the authors prove that the commutator [b,I
α
] is a compact operator from the Morrey space L
p, λ
(ℝ
n
) to L
q, λ
(ℝ
n
) if and only if b ∈ VMO(ℝ
n
), the BMO-closure of .
The research was supported by NSF of China (Grant: 10571015, 10826046) and SRFDP of China (Grant: 20050027025). 相似文献
20.
概率赋范空间中的非线性半群与微分包含* 总被引:1,自引:0,他引:1
本文的目的是在概率赋范空间中引入和研究非线性压缩半群,并对增生映象建立Crandal-Ligget指数公式.作为应用,我们将应用这些结果研究概率赋范空间中一类具增生映象的微分包含的Cauchy问题解的存在性. 相似文献