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

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这是为参加1996年8月17日至8月27日在爱琴海大学举行的“爱琴海算子代数与应用会议”的初级研究人员和研究生提供旅费的请求。随着算子空间理论的出现，也被称为“量子化泛函分析”，一般的、不一定自伴随的算子代数已经取得了与自伴随算子代数相当的本体论地位。虽然从某些角度来看，非自伴随理论还没有发展得很好，但在过去六年左右的时间里，研究结果的爆炸式增长值得以一种方式进行展示，使外行人，特别是年轻的学者，能够从当前的角度轻松地了解该学科的基础知识。会议的目的是提供一系列即将出版的短期课程，旨在提供非自伴随算子代数理论的概述及其与算子代数和现代分析的其他领域的关系。要强调的主题是：非自伴随算子代数，一般理论；具体算子代数，特别是自反代数；多变量算子理论与函数代数的表示代数主题的度量变化-希尔伯特和算子模；算子空间及其在巴拿赫空间理论和调和分析中的应用量子群的算子代数方法非自伴随算子代数与小波。非自伴随算子代数理论在许多应用于国家需要领域的数学基础中起着核心作用。例如，在信号处理领域，用于传输涉及所有科学领域的数据和图像-从空间天文台到大脑的断层扫描-基本结构，如所谓的Toeplitz矩阵和小波变换，获得了最深刻的意义，从算子代数的角度来看，最清楚地揭示了这一点。算子代数揭示了它们的基本代数性质（它们在实践中是如何被操作的）和度量性质（它们是如何被测量的）。在石油勘探中，涉及到小波和不同方式的信号处理，算子代数方法（称为交换提升）起着基本的作用。此外，在控制理论中，特别是在飞机和降噪器的设计中，所涉及的数学在很大程度上是算子代数。大约六年前发生的突破，以及上面提到的，使这一领域的实践者能够有效地发挥现代代数的全部力量来解决最基本和最基本的结构问题。这一领域的进展非常令人兴奋，未来还会有更多的进展。但是现在是时候收集已知内容的摘要了，包括参考书目，这样新人就可以进入这个令人兴奋的新兴研究领域。