局部凸空间下Minkowski泛函的Gateaux可微点及Frechet可微点的特征

局部凸空间下Ｍｉｎｋｏｗｓｋｉ泛函的Ｇａｔｅａｕｘ可微点及Ｆｒｅｃｈｅｔ可微点的特征武俊德，李燕杰，吴继周（大庆石油学院）在建立局部凸空间几何理论过程中，一个基础工作是给出Ｍｉｎｋｏｗｓｋｉ泛函的Ｇａｔｅａｕｘ可微点和Ｆｒｅｃｈｅｔ可微点的特征。本文...     

Mutual Information and Relative Entropy of Sequential Effect Algebras

In this paper, we introduce and investigate the mutual information and relative entropy on the sequential effect algebra, we also give a comparison of these mutual information and relative entropy with the classical ones by the venn diagrams. Finally, a nice example shows that the entropies of sequential effect algebra depend extremely on the order of its sequential product.     

用Riemann积分给出Lebesgue积分的新定义——应用泛函分析教学札记

<正> 在传统的Lebesgue积分教学中,需要花费相当的时间先介绍测度理论。但是苦于目前各院校开设应用泛函分析的学时不足,在教学中存在一定的困难。我们采用郑维行、王声望二位先生“积分是高一维的测度”的观点,同时也不同于黎茨、纳吉的论述,直接由Riemann     

具有弱滑脊性质序列空间上的HelingerToeplitz定理

设Ｅ（Ｘ）和Ｆ（Ｙ）是向量值序列空间并且Ｅ（Ｘ）具有弱滑脊性质．Ａ＝［Ａｉｊ］是一个算子值无穷矩阵并且映Ｅ（Ｘ）进入Ｆ（Ｙ）．如果（Ｘ，Ｙ）有Ｂａｎａｃｈ－Ｓｔｅｉｎｈａｕｓ性质，那么Ａ是σ（Ｅ（Ｘ），Ｅ（Ｘ）βＹ）－σ（Ｆ（Ｙ），Ｆ（Ｙ）βＹ）连续的．     

RESEARCH ANNOUNCEMENTS The New Necessary and Sufficient Conditions for the Uniformly Continuous and Continuous of Duality Mappings

In[1],Ma shaoqin gave the necessary and sufficient condition for the uniformlycontinuous and continuous of duality mappings.In the note,We give very simplecriteria for the uniformly continuous and continuous of duality mappings.And by[1],the necessary and sufficient conditions for the norm of a real Banach Space to beuniformly Frechet differentiable and Frechet differentiable are described.     

一致凸度量线性空间的自反性及其应用

为研究度量线性空间中凸集的逼近性质，Ｇ．Ｃ．Ａｈｕｊａ等引起了度量线性空间的严格凸性及一致凸性的定义。本文证明了完备的一致凸的度量线性空间是自反的。同时，作为应用，研究了最佳联合逼近元的存在性与唯一性问题。     

2×2-上三角算子矩阵谱的Fredholm扰动

设H和K是复无穷维可分Hilbert空间,A∈B(H),B∈B(K),C∈B(K,H)且M_C=(ACOB).本文给出了上三角算子矩阵M_C的Weyl谱、本性谱、谱、左谱、右谱、下半本性谱、下半Weyl谱和上半Weyl谱的Fredholm扰动的完全刻画.