Mathematical Sciences: Problems in Modern Analysis

数学科学：现代分析中的问题

• 批准号: 9401582
• 负责人: Per Enflo
• 金额: $ 12.55万
• 依托单位: Kent State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-06-01 至 1998-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9401582&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Problems; Modern; Analysis

9401582 Enflo The proposers plan to work on two projects involving bounded operators on Hilbert space. The first project is to study orbits of cyclic vectors of operators. In particular, different regularity properties of these orbits. The second project involves a study of some aspects of invariant subspaces using recently developed techniques of the proposers. The focus here is on quasinilpotent operators. Operators on Hilbert space represent an infinite dimensional generalization of matrices. It is a well known fact that given a matrix there is always a vector such that the span of iterates of the matrix action on this vector is not the whole vector space. This project is focused on the analogous question in the infinite dimensional case. Appropriately formulated, this question is called the invariant subspace problem. It has been the focus of much research on operator theory. The question is an attempt to decompose operators into building `locks and is central to the analysis of the structure of operators. ***

小行星9401582 提议者计划在希尔伯特空间上进行两个涉及有界算子的项目。第一个项目是研究算子循环向量的轨道。特别是，这些轨道的不同规律性。第二个项目涉及的一些方面的研究不变的子空间使用最近开发的技术的提案人。这里的重点是拟幂零算子。 希尔伯特空间上的算子表示矩阵的无限维推广。众所周知，给定一个矩阵，总有一个向量，使得矩阵作用在这个向量上的迭代的跨度不是整个向量空间。 这个项目的重点是在无限维的情况下类似的问题。适当地表述，这个问题被称为不变子空间问题。它一直是算子理论研究的焦点。这个问题是试图将操作符分解为构建“锁”，并且是分析操作符结构的核心。 ***