取值于Banach空间的序列空间的广义Kothe对偶(英文)

The theory of Kothe sequence spaces with values in a scalar field has been considerably developed (for example, see Ruckle, W, H, Sequence Spaces, London, 1981). In this paper, the generalized Kothe duals of sequence spaces with values in a Banach space are defined, and some properties of the duals are given. Let X be a Banach space with the norm ‖·‖and X', its topological dual, and X~N, (X')~N the spaces of all sequences in X and X' respectively, and φ(X), φ(X') the spaces of all finite sequences in X and X' respectively.     

Banach空间中的条件(dc)

为了研究Banach空间中有界闭集满足(dc)的条件,依据条件(dc)在Banach空间中低维有界闭集的完备化过程中的相关理论,给出了有界闭集满足(dc)的一个必要条件和有界闭集满足(dc)的一个充分条件.这一充分条件改进了Papini和吴森林给出的有界闭集满足(dc)的两个充分条件.     

Banach空间上的算子空间的若干性质

本文在Ｂａｎａｃｈ空间上研究算子子空间的性质Ｃ及Ｃσ性质     

关于双参数半群的预解式(1)(英文)

Let B be a Banach space. {T_(s,t),00, s<0). Then {Q_(λ,s),λ>0, s>0}and {R_(λ,s), λ>0, s>0). Then {Q_(λ,s), λ>0, s>0} and {R_(λ,s), λ>0,s>0} are said to be the left and right resolvent of {T_(s,t)} respectively.     

关于双参数半群的预解式(2)(英文)

This paper is a continuation of the paper [1]. In this paper, we introduce the concept of the left double resolvent of a two-parameter semigroup, and obtain some results. Theorem 1 Let B be a Benach space. {T_(s,t)} be a two-parameter contraction     

Marcinkiewicz 空间 M(α)的子空间 E_(M(α)) 的刻化

讨论了Ｍａｒｃｉｎｋｉｅｗｉｃｚ空间Ｍ（α）的子空间ＥＭ（α）的结构和性质，给出了Ｍ（α）空间连续线性泛函的一般表达式。     

Banach空间Co上的弱紧算子

利用矢值序列空间为工具证明了Ｂａｎａｃｈ空间Ｃｏ上的每个弱紧算子是紧算子。     

关于邻近空间的特征(英文)

Because the contiguous space is a generalization of the uniform space, which has some of its characteristics. However, the conditions for a contiguous space are not so rigorous as that for a uniform space. This is the reason why people are absorbed in studying the relations between its structure and topology, and expect it will be applied on a wide scale, This paper discusses the structure of the contiguous space from three different angles.     

Banach空间上非线性映照的遍历收敛定理

X是Banach空间，（X，τ）是局部凸线性拓扑空间，C是X上的广序列紧凸集，T是C上的渐近非扩张映照并且具有性质（Г）．在一致τ-opial条件下给出了渐近非扩张映照的遍历收敛定理并进行了证明．该结论首次在Banach空间中给出了遍历收敛定理，因而定理推广了近期相关的一系列研究成果．     

Hilbert空间上最终范数连续半群的扰动

在算子半群扰动的基础上,对一类型半群即最终范数连续半群的扰动进行了研究,得到了Hilbert空间中最终范数连续半群的一个新的扰动结果,使得半群扰动的结果更加丰富.     

Banach空间上广义p-正常算子的注记

广义p-共轭算子和广义p-正常算子的概念在文献和中分别引入。本文中,我们得出拟相似广义p-正常算子的一个谱性质以及广义p-正常算子亦有(Ac)性质;我们证明了广义p-自伴算子是纯量型谱算子。从而回答了D.K.Scn提出的一个问题[5,Note2.26].     

(QL)型Fuzzy拓扑线性空间的乘积和商空间(英文)

In this paper, we have got some properties of product and quotient spaces of fuzzy topologioal vector spaces of type (QL) (cf. Wu Congxin, Fang Jinxuan, Annals of Math., 6A (1985), 3: 355-364), whereby we work out a representation theorem of locally ccnvex spaces. Fuzzy topological vector space is short for FTVS in the following text. Lemma 1. Let (X,T) be a FTVS of type (QL) and {‖·‖_d: d∈D} be the family of Lasalle pseudonorms generating T, then the fuzzy net {X_(λα)~((α)): α∈A} converges to x_λiff for each ε>o, o<δ<λand ‖·‖_d, there exists α∈A such that ‖x-x_(λn)~((n))‖_d<ε, λ_n>λ-δwhenever n≥α. Let (X,T) be the product space of a family of FTVSs(X_α,T_α) (a∈A); P_α     

Banach空间闭集上的具有不连续右端的微分方程(Ⅰ)

本文研究Banach空间中闭集F上的常微分方程的Cauchy问题,x′=f_0(t,x),x(t_0)=x_0。得到了由这类方程所描述的Carathéodory系统解的存在性和唯一性定理。     

cmc(X)为GAK—空间的特征(英文)

Let X be a locally convex space and X~* its dual space.Let N(X) denote a localbase neighborhoods 0∈X which are barrells.For each U∈N(X),letP_U(x)=sup{|f(x)|:f∈U~0}, (?)x∈X,where U~0 is polar of U with respect to the dual pair (X, X~*).Then P_U is a continuousseminorm on X. Pietsch gave the vector-valued sequence space l_1[X] as follows:     

复Banach空间上推广的Roper-Suffridge算子的性质

讨论复Banach空间上两类推广的Roper-Suffridge算子,证明该算子保持强β型螺形映照、强α次殆星映形照、α次强β型螺形映照及α次殆β型螺形映照的性质,并作为特殊情况包含了已有的结论.     

二次函数方程在Schwartz广义函数空间D′(R~n)上的稳定性(英文)

利用广义函数正则化的方法研究了二次函数方程在Schwartz广义函数空间D′(Rn)上的Hyers-Ulam-Rassias型稳定性,并得到了类似于在一般函数空间上的二次函数方程稳定性结果.     

Banach格上正则AM-紧算子的AM-空间

给出Banach格上所有从E到F的正则AM-紧算子空间在||·||AM范数下是AL-空间,当且仅当E是AM-空间,且F是AL-空间;正则AM-紧算子空间在||·||AM范数下是AM-空间,当且仅当E是AL-空间,F是AM-空间。     

Banach空间柱形域上微分方程解的存在性

讨论Banach空间柱形域上摄动微分方程解的存在性,证明了关于局部解、整体解及周期解的一些结论,推广并完善了文献[6.8.9]等中的结果。     

一致凸Banach空间上的公共不动点及其结构

首先在映射对是半紧的假设下得到了公共不动点的两个存在定理，然后进一步研究了公共不动点的一个构造方法———即Ｉｓｈｉｋａｗａ迭代法     

集值映射空间及其性质(英文)

1 The contiguons spaces and contiguous mapping Definition 1.1 Let X be a non-void set, V be a non-void subsets of X×X, such that