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

小行星9622991 这是为初级研究员和研究生参加定于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和应用会议提供旅费支助的请求。 随着算子空间理论的出现，也被称为“量化泛函分析”，一般的，不一定自伴的算子代数已经达到了与自伴算子代数相当的本体论地位。 虽然非自伴理论还没有得到很好的发展，但从某些角度来看，在过去六年左右发生的结果爆炸，值得以一种让外行，特别是年轻学者，从当前的角度轻松获得该主题的基础知识的方式曝光。 会议的目的是提供一系列的短期课程，这将是出版，旨在提供非自伴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：非自伴算子代数，一般理论;具体的算子代数，特别是自反代数;多变量算子理论和函数代数的表示;度量变化的主题从代数-希尔伯特和运营商模块;运营商空间及其应用Banach空间理论和调和分析;运营商代数方法量子群;非自伴算子代数和小波。 非自伴算子代数的理论在许多应用于国家需要的数学领域的数学基础中起着核心作用。 例如，在信号处理领域，它被用来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，获得其最深刻的意义，并在从算子代数的角度来看时最清楚地揭示。 算子代数揭示了它们的基本代数性质（在实践中如何操作它们）和度量性质（如何测量它们）。 在石油勘探中，涉及小波和信号处理在某种程度上不同的方式，算子代数方法，被称为交换提升发挥了重要作用。 此外，在控制理论中，特别是在飞机和消声器的设计中，所涉及的数学在很大程度上是算子代数。 突破，发生在大约六年前，并提到以上，使从业者的这一领域带来裸露有效的全部力量现代代数来解决最基本和根本的结构问题。 这一领域的进展非常令人兴奋，而且还会有更多的进展。 但现在是时候收集已知的摘要，包括参考书目，以便新人可以进入这个令人兴奋的新兴研究领域。

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.