Mathematical Sciences: Aegean Conference in Operator Algebras and Application; August 17-27, 1996; Athens, Greece

数学科学：爱琴海算子代数及应用会议；

• 批准号: 9622991
• 负责人: Paul Muhly
• 金额: $ 1万
• 依托单位: University of Iowa
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-08-01 至 1997-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9622991&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Aegean; Conference; Operator; Mathematical; Sciences; Aegean; Conference; Operator

9622991 MUHLY This is a request for travel support for junior investigators and graduate students to attend the conference, Aegean Conference in Operator Algebras and Applications, that is scheduled for the period, August 17, 1996, to August 27, 1996, at the University of the Aegean. With the advent of the theory of operator spaces, also known as "quantized functional analysis", general, not-necessarily-self-adjoint, operator algebras have achieved an ontological status comparable to that held by the self-adjoint operator algebras. Although the non-self-adjoint theory is not yet as well developed, from certain perspectives, the explosion of results that has taken place in the last six years, or so, deserves to be exposed in a fashion that will allow the uninitiated, particularly younger scholars, easy access to the basics of the subject from the current perspective. The objective of the conference is to provide a series of short courses, that will be published, designed to provide an overview of the theory of non-self-adjoint operator algebras and its relation to other areas of operator algebra and modern analysis. The themes to be stressed are: non-self-adjoint operator algebras, general theory; concrete operator algebras, particularly reflexive algebras; multivariable operator theory and representations of function algebras; metric variations on themes from algebra - Hilbert and operator modules; operator spaces and their applications to Banach space theory and harmonic analysis; operator algebraic approaches to quantum groups; non-self-adjoint operator algebras and wavelets. The theory of non-self-adjoint operator algebras plays a central role in the mathematical underpinnings of a lot of mathematics applied to areas of national need. For example, in the area of signal processing, which is used to transmit data and images involved in all fields of science - from space observatories to tomographs of the brain - fundamental constructs, such as the so-calle d Toeplitz matrices and wavelet transforms, obtain their deepest significance and are most clearly revealed when viewed from the perspective of operator algebra. Operator algebra lays bare their basic algebraic properties (how they are manipulated in practice) and metric properties as well (how they are measured). In oil exploration, which involves wavelets and signal processing in a somewhat different fashion, operator algebraic methods, known as commutant lifting play a fundamental role. Also, in control theory, particularly in the design of aircraft and noise abaters, the mathematics involved is to a large extent operator algebra. The breakthrough that took place about six years ago, and alluded to above, enables the practitioner of this field to bring to bare effectively the full power of modern algebra to tackle the most basic and fundamental structural questions. The advances in this field have been very exciting and more are to come. But it is time collect a summary of what is known, including bibliographies, so that new people can enter this exciting, emerging field of research.

9622991 Muhly这是为初级调查人员和研究生参加会议的要求提供旅行支持，即安排在1996年8月17日至1996年8月27日在AEEGEAN大学的这一期间的AEEGEAN OEGEAN会议。 随着操作员空间理论的出现，也称为“量化功能分析”，一般，不必要的偶像，操作员代数实现了与自我联合操作员代数相当的本体论状态。 尽管从某些角度来看，非自我伴侣理论尚未达到良好的发展，但在过去六年中发生的结果的爆炸爆炸值得以一种允许未经启发的，尤其是年轻的学者，从当前的角度来访问该主题的基础知识的方式。 会议的目的是提供一系列简短的课程，这些课程将出版，旨在提供非自我支持操作员代数及其与其他操作员代数和现代分析的关系的概述。 要强调的主题是：非自我支持操作员代数，一般理论；混凝土操作员代数，尤其是反射代数；函数代数的多变量运算符理论和表示；来自代数希尔伯特和操作员模块的主题的度量变化；操作员空间及其在Banach空间理论和谐波分析中的应用；量子组的操作员代数方法； 非自动联合操作员代数和小波。 非自我支持操作员代数的理论在适用于国家需求领域的许多数学的数学基础中起着核心作用。 例如，在信号处理领域（用于传输各个科学领域的数据和图像 - 从太空观测器到大脑的层表 - 基本构造，例如So -Calle d toeplitz矩阵和小波的矩阵变换，并在观察经营者Algebra的角度观看时获得最深的意义，并且最清楚地揭示了它们。 操作员代数揭示其基本代数特性（在实践中如何操纵）和度量特性（如何测量它们）。 在涉及小波和信号处理的石油探索中，操作员代数方法（称为换向提升）起着基本作用。 同样，在控制理论，尤其是在飞机和噪声降低器的设计中，所涉及的数学在很大程度上是操作员代数。 大约六年前发生的突破，并提到上述，使该领域的从业者能够有效地实现现代代数的全部力量，以解决最基本和最基本的结构问题。 该领域的进步非常令人兴奋，还将有更多的进步。 但是现在是时候收集包括书目在内的已知知识的摘要，以便新人们可以进入这个令人兴奋的新兴研究领域。