Banach space structures of L^p-spaces and non-commutative Hardy spaces

L^p 空间和非交换 Hardy 空间的 Banach 空间结构

• 批准号: 0096696
• 负责人: Narcisse Randrianantoanina
• 金额: --
• 依托单位: Miami University
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-07-01 至 2005-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0096696&HistoricalAwards=false
• 关键词: Banach; space; structures; spaces; non

The proposed research will focus on problems concerning Banach space theory and its connections with operator algebras and operator theory. The main aim of this research is the investigation of structures of non-commutative L^p-spaces and non-commutative Hardy spaces. The basic permanence question in this direction of research is wether or a given property can be lifted from a given function space to its non-commutative version. One of the questions that will be considered is the classification of non-commutative spaces according to type and cotype. Another significant question is whether or not reflexive subspaces of preduals of von Neumann algebras have the fixed point property. Basic Banach space structure of the newly defined script-L^p-spaces and severalnon-commutative generalizations of Hardy spaces are at the center of this investigation. Another direction of research to be considered is the study of ideals of operators on C*-algebras.This proposal represents work of an interdisciplinary nature on mathematical analysis. Banach space theory, which is the main topic of this proposal, studies notions of distances on infinite dimensional vector spaces. It provides general framework for several fields of mathematics. The theory of function spaces played a crucial role in the development of Banach space theory for several decades. The current project studies a relatively new concepts of non-commutative analog of function spaces in which functions are replaced by operators. These spaces includes C*-algebras, preduals of von Neumann algebras among many others. C*-algebras turn out to be one of the mostimportant structures in mathematics. They have significant applications to other parts of sciences (for examples, geometry, mathematical physics and quantum mechanics), so it is important to consider them from many different point of view. In this case as Banach spaces.

拟议的研究将重点介绍有关Banach空间理论及其与操作员代数和操作员理论的联系的问题。这项研究的主要目的是研究非交互性l^p空间和非交互性耐寒空间的结构。在这个研究方向上的基本持久性问题是，或者可以将给定的属性从给定的功能空间提升到其非交换版本。将要考虑的问题之一是根据类型和cotype对非交流空间进行分类。另一个重要的问题是von Neumann代数的预期反射子空间是否具有固定点特性。新定义的脚本l^p空间的基本BANACH空间结构和Hardy空间的多个共同概括是本研究的中心。要考虑的研究的另一个方向是对c*orgebras的操作员理想的研究。该提案代表了数学分析的跨学科性质的工作。 Banach空间理论是该提案的主要主题，研究了无限维矢量空间的距离概念。它为数学领域提供了一般框架。数十年来，功能空间理论在Banach空间理论的发展中起着至关重要的作用。当前的项目研究了功能空间的非共同类似物的相对较新的概念，其中功能被操作员替换。这些空间包括C* - 代数，冯·诺伊曼代数的预期。 C* - 代数被证明是数学中最重要的结构之一。它们在科学的其他部分（例如，几何，数学物理学和量子力学）中具有重要的应用，因此从许多不同的角度考虑它们很重要。在这种情况下，作为Banach空间。