Banach * 代数

Ｖ．Ｐｔáｋ［１］在有单位元的情形下详细研究了Ｂａｎａｃｈ代数．本文将推广他的结果到一般情形．特别，我们引入了可正开拓的正线性泛函，并对它进行了刻划．     

Banach空间具有Banach—Saks性质的一个充分条件

本文的目标是利用凸性指标给出Ｂａｎａｃｈ空间具有Ｂａｎａｃｈ－Ｓａｋｅ性质的一个充分条件，从而推广Ｋａｎｋｕｔａｎｉ定理。     

Banach空间上Banach框架和原子分解的扰动

框架扰动是框架理论中活跃的研究方向, 但它的多数研究是在Hilbert空间上进行的. 该文讨论Banach空间上Banach框架和原子分解的扰动, 得到一些新的结果, 并表明众多已知结果是这些新结果的特例.     

Banach空间上的Banach框架及原子分解的稳定性

讨论了Banach空间上的Banach框架及原子分解的稳定性,得到了一些新的结果,并给出一些已知结果的推论.     

Banach流形上映射度

本文讨论一种无限维流形上拓扑不变量，即具有可定向Ｆｒｅｄｈｏｌｍ结构的实Ｂａｎａｃｈ流形上　　Ｃｒ　　映射度．它是通常有限维流形上光滑映射度的一种自然推广．     

Very Convex Banach Spaces

ＶｅｒｙＣｏｎｖｅｘＢａｎａｃｈＳｐａｃｅｓＴｅｇｕｓｉ（特古斯）Ｓｕｙａｌａｔｕ（苏雅拉图）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＩｎｎｅｒＭｏｎｇｏｌｉａＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｈｕｈｈｏｔ，０１００２２）ＬｉＹｏｎｇｊｉｎ...     

平的Banach空间

本文定义了平的Ｂａｎａｃｈ空间，证明了平的Ｂａｎａｃｈ的空间Ｘ的共轭空间Ｘ没有非常光滑点，而Ｓ（Ｘ）的非光滑点在Ｓ（Ｘ）是稠密的，同时还给出Ｘ具有粗范数的一个充分条件。     

Wiener型Banach代数

对G-完全对称的Banach代数给出了清晰的刻画, 特别引入了Wiener型Banach代数, 刻画了其结构并给出了有关应用.     

论顺从Banach代数

In this paper we extend the concept of amenable algebra given by Johnson in [ 3 ] to n-amenable algebra. We prove several properties which are extension of 1-amenable algebras appeared in [3] and [4], and we give a sufficient condition for a Banach algebra being 2- amenable.     

Banach空间微分方程初值问题

利用半序理论及单调迭代方法研究了Banach空间中非线性微分方程初值问题解的存在惟一性以及解的迭代逼近与误差估计。     

On Amenable Banach Algebras

In this paper we extend the concept of amenable algebra given by Jobnsonin[3]to n-amenable algebra.We prove several properties which are extensionof1-amenable algebras appeared in[3]and[4],and we give a sufficientcondition for a Banach algebra being2-amenable.     

L~P-orthogonality in Banach Spaces

The notion of L~P-orthogonality was posed by F. Sullivan [1], but it hadnever been studied. The purpose of this paper is to give some results concerningthe L~P-orthogonality in Banach spaces.     

A construction of ℒ∞-spaces and related Banach spacesand related Banach spaces

Let λ>1. We prove that every separable Banach space E can be embedded isometrically into a separable ℒ _∞ ^λ -spaceX such thatX/E has the RNP and the Schur property. This generalizes a result in [2]. Various choices ofE allow us to answer several questions raised in the literature. In particular, takingE = ℓ₂, we obtain a ℒ _∞ ^λ -spaceX with the RNP such that the projective tensor product containsc ₀ and hence fails the RNP. TakingE=L ¹, we obtain a ℒ _∞ ^λ -space failing the RNP but nevertheless not containingc ₀.     

A Banach–Zarecki Theorem for functions with values in Banach spaces

A Banach–Zarecki Theorem for a Banach space-valued function  \(F : [0,1] \rightarrow X\) with compact range is presented. We define the strong absolute continuity ( \(sAC_{||.||_{F}}\) ) and the bounded variation ( \(BV_{||.||_{F}}\) ) of \(F\) with respect to the Minkowski functional \(||.||_{F}\) associated to the closed absolutely convex hull \(C_{F}\) of \(F([0,1])\) . It is proved that \(F\) is \(sAC_{||.||_{F}}\) if and only if \(F\) is \(BV_{||.||_{F}}\) , weak continuous on \([0,1]\) and satisfies the weak property \((N)\) .     

Banach空间的型与独立Banach空间值随机变量序列的不等式

本文建立了独立Ｂ值随机变量序列部分和的极大值函数Ｓ＊与ｐ方根函数Ｓ（ｐ，Ｘ）的分布函数不等式与矩不等式，讨论了这些不等式的成立与Ｂａｎａｃｈ空间的ｐ型与ｑ余型的关系，同时给出了与Ｈｉｌｂｅｒｔ空间同构的Ｂａｎａｃｈ空间的特征。     

Banach空间的某类分解

该文从Schauder分解出发，考虑了由一类具有特殊基的Banach空间Y所生成的Banach空间Y（Xi，i∈N）（特别是当每个Xi均为Y的标量域）的一些性质，以及它们之间的联系．     

关于凸的Banach空间

本文给出可数个 P 凸的 Banach 空间的l_p,(1相似文献   

Generic Hahn–Banach results

Given f:X→R∪{+∞}$f:X\to \mathbb{R}\cup \{+\infty \}$ a convex and lower semi-continuous function defined on a reflexive Banach space X, and L, a closed linear manifold of X over which f takes at least a real value, the aim of this note is to prove the following Baire category result: in the Euclidean setting, the set of affine functions dominated by f on L for which there is no dominated extension to X is always of first Baire category, but this set can be as large as a residual set, provided that X is a reflexive Banach space of infinite dimension.     

Banach空间中的非线性边值问题

本文考虑Ｂａｎａｃｈ空间中形如“ｘ（ｎ）—Ａｉ（ｔ）ｘ（ｉ－１）＝ｆ（ｔ，ｘ，ｘ＇，…，ｘ（ｘ－１））（０≤ｔ≤１），Ｂｘ＝ξ”的非线性边值问题，利用关于全连续映射的一定不动点定理给出了以上问题有解的充分条件．