Research on Geometry and Probability in Banach Spaces and its Applications

Banach空间中的几何与概率研究及其应用

基本信息

批准号：
09640214
负责人：
TAKAHASHI Yasuji
金额：
$ 1.92万
依托单位：
Okayama Prefectural University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 1998
项目状态：
已结题

项目摘要

We considered some generalizations of classical norm inequalities in general Banach spaces from the operator theoretical and probability theoretical point of view, and using these inequalities we investigated functional-analytic, geometric and probabilistic properties of Banach spaces as well as the relations between these properties.The main results obtained here are as follows.1. Clarkson-type inequalities and geometry of Banach spaces :(1) High-dimensional versions of the Clarkson inequality (CI) are given in the general Banach space setting from the probability theoretical point of view. In particular, a characterization of (CI) is given by the notions of Rademacher type and cotype.(2) It is shown how Clarkson-type inequalities are inherited by the Lebesgue-Bochner spaces L_r (X) from a given Banach space X.(3) Geometrical properties of Banach spaces are characterized using Clarkson-type inequalities.2. Hanner, Hlawka and the other inequlities in Banach spaces : High-dimensional versions of hanner and Hlawka inequalities are given from the probability theoretical point of view, and geometric and probabilistic properties of spaces are described by these inequalities and the others.3. Von Neumann-Jordan (NJ-) constant and geometry of Banach spaces : Some geometrical constants of Banach spaces X including NJ-constant C_<NJ>(X) and James constant J(X) are introduced, and geometrical properties of X are described in terms of these constants.4. Applications to Banach space theory and other related areas : Some properties of functional analysis are investigated in connection with geometric and probabilistic properties. Some applications to vector valued ergodic theorems are also investigated.

我们考虑了从操作员的理论和概率理论的角度来考虑一般Banach空间中经典规范不平等的一些概括，并且使用这些不平等，我们研究了Banach空间的功能分析，几何，几何和概率的特性以及这些属性之间的关系。 Clarkson型的不平等和BANACH空间的几何形状：（1）Clarkson不平等的高维版本（CI）是从一般Banach空间设置中从概率的理论观点中给出的。特别地，（CI）的表征由Rademacher类型和Cotype的概念给出。（2）显示了Lebesgue-Bochner空间L_R（X）从ivjing Banach Space X中继承了Clarkson-type的不平等。 Banach空间中的Hanner，Hlawka和其他不合格：Hanner和Hlawka不平等的高维版本是从概率理论的角度来看，这些不平等现象的几何学和概率特性描述了这些不平等现象。 von Neumann-Jordan（nj-）常数和Banach空间的几何形状：引入了Banach空间X的一些几何常数，包括NJ-Constant C_ <nj>（X）和James Constant J（X），并用这些常数的术语描述了X的几何特性。在Banach空间理论和其他相关领域的应用：与几何和概率特性有关的功能分析的某些特性。还研究了对矢量有价值的千古定理的某些应用。