RESEARCH ON GEOMETRIC STRUCTURES OF BANACH AND FUNCTION SPACES AND ψ-DIRECT SUMS

Banach几何结构与函数空间及ψ-直和的研究

基本信息

批准号：
18540185
负责人：
KATO Mikio
金额：
$ 2.48万
依托单位：
Kyushu Institute of Technology
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2006
资助国家：
日本
起止时间：
2006 至 2007
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-18540185/
关键词：
ψ-direct sum of Banach spaces fixed point property normal structure weak nearly uniform smoothness uniform non-l^n_1-ness von Neumann-Jordan type constant sharp triangle inequality Banach spaces バナッハ空間のψ直和 uniform non-l^n_1-ness Weak n

项目摘要

Geometric structures of Banach and function spaces and also ψ-direct sums of Banach spaces are investigated. Major results are as follows.(1)A sharp triangle inequality and its reverse inequality with n elements were obtained, where some conditions for equality attainedness were presented. We used them to investigate the uniform non-l^n_1-ness etc. of Banach spaces. We extended these inequalities and also we had some results on such type inequalities with a parameter.(2)Since it was introduced by the author etc. in 2002, the-ψ-direct sums have been attracting a good deal of attention. In this research project we obtained a sequence of results on the-ψ-direct sums concerning weak nearly uniform smoothness, WORTH property, Schur property, and uniform non-l^n_1-ness etc. As extreme cases some interesting results on l_1 and l_∞-sums are included: In particular we constructed uniformly non-l^3_1 Banach spaces which are not uniformly non-square, but have the fixed point property for non-expansive mappings (resp. but are super-reflexive).(3)We introduced the von Neumann-Jordan type and the James type constants and obtained several results on the uniform non-squareness and uniform normal structure etc. with these constants. Also we obtained some results on the weak modules of nearly uniform smoothness.(4)In July, 2007 the head investigator participated in the International Workshop on Banach space, Operator Theory and Applications to Nonlinear Analysis held in Harbin, China and presented an invited talk and a special lecture for graduate students, where he introduced some recent results on the-ψ-direct sums of Banach spaces. We organized the Second International Symposium on Banach and Function Spaces 2006in September, 2006, Kitakyushu, Japan, and its proceedings Banach and Function Spaces II (pp.467)was published by Yokohama Publishers in 2008.

研究了Banach和功能空间的几何结构，以及Banach空间的ψ-导向总和。主要结果如下。（1）获得了急剧的三角形不平等及其与n个元素的反向不平等，其中提出了一些平等的条件。我们用它们研究了Banach空间的均匀非l^n_1-度等。我们扩大了这些不平等，也有一些与参数的类型不等式的结果。（2）由于作者是由作者引入等。2002年，单次直接款项吸引了很多关注。在该研究项目中，我们获得了一系列关于单艇的成果的顺序，涉及弱几乎均匀的平滑度，价值，schur属性和统一的非l^n_1-度等。作为极端情况，包括在L_1和L_1和L_∞-SUMS上进行一些有趣的结果：包括：特别是我们构建了均匀的非^3_1 Banach空间，但不统一地授权，但不合身，但不合格，但是不合身的，但是不合身的，但是不合身的，但是不合身的，但是不合身的。（3）我们引入了von Neumann-Jordan类型和James类型常数，并使用这些常数获得了一些关于均匀的非质量和均匀的正常结构等的结果。（4）2007年7月，我们还获得了一些弱模块。（4）首席调查员参加了关于Banach空间，操作员理论和应用在中国Harbin举行的非线性分析的国际研讨会，并为研究生提供了一场邀请的演讲，并为研究生提供了一些有关Banrach领域的最新成绩。我们组织了2006年9月在日本Kitakyushu的Banach and Function Spaces 2006年的第二次国际研讨会，其会议记录Banach and Function Spaces II（pp.467）于2008年发表。