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.

拟议的研究将集中在有关问题的Banach空间理论及其与算子代数和算子理论的联系。本文主要研究非交换L^p-空间和非交换哈代空间的结构。这个研究方向的基本持久性问题是给定的属性是否可以从给定的函数空间提升到其非交换版本。将考虑的问题之一是根据类型和cotype对非交换空间进行分类。另一个重要的问题是von Neumann代数的预映射的自反子空间是否具有不动点性质。新定义的脚本-L ^p-空间的基本Banach空间结构和哈代空间的几个非交换推广是本文研究的中心。另一个要考虑的研究方向是研究C*-代数上算子的理想。这个建议代表了数学分析的跨学科性质的工作。巴拿赫空间理论，这是本提案的主要议题，研究无限维向量空间的距离概念。它为数学的几个领域提供了一般框架。函数空间理论在Banach空间理论的发展中起了至关重要的作用几十年。目前的项目研究了一个相对较新的概念，非交换模拟的功能空间，其中功能被取代的运营商。这些空间包括C*-代数，冯诺依曼代数的前身。C*-代数是数学中最重要的结构之一。它们对其他科学领域（例如几何学、数学物理学和量子力学）有重要的应用，因此从许多不同的角度考虑它们是很重要的。在这种情况下是Banach空间。