Fourteenth International Conference on Banach Algebras

第十四届巴拿赫代数国际会议将于1999年7月25日至8月7日在加州克莱蒙特的波莫纳学院举行。本系列会议强调巴拿赫代数及其与其他分析领域的联系。这次会议的题目是“巴拿赫代数和巴拿赫空间上的算子”。正式的会议计划将包括大约六十场关于巴拿赫代数的一般理论、具体的巴拿赫代数以及相关分析领域的演讲。在会谈中将强调的一些领域包括自动连续性，可调性和Banach同调，Banach代数的结构，谱理论和算子理论，群代数和其他卷积代数，以及复解析方法。现代数学的伟大成就之一是抽象。就像初等代数对算术的推广一样，抽象不仅使数学家能够解决单个问题，而且还能解决整个问题。20世纪最重要的例子之一是功能分析领域。功能分析使用新的抽象技术来处理问题，这些问题已经被我们现在所说的经典分析研究了200多年，经典分析是由微积分发展而来的方法的集合。功能分析不是集中研究单个功能，而是研究功能的空间和这些空间的抽象。通过新旧方法的结合，不仅可以解决新问题和以前难以解决的老问题，而且功能分析的新结构还提供了一种新的语言，用于表达现代物理学以及后来其他科学领域和经济学的许多结果。功能分析所考虑的空间都有某种形式的加法运算，但许多最重要的空间也有其他运算。特别是，巴拿赫代数和相关领域涉及到非常大而重要的问题和结构集合，这些问题和结构具有某种乘法和通常的加法。到20世纪60年代，会议的主题巴拿赫代数已经成为公认的数学领域。自1974年以来，巴拿赫代数的定期国际会议已成为世界各地的研究人员了解该领域，发起和继续研究合作，并与相关领域的研究人员交流思想的重要途径。

The Fourteenth International Conference on Banach Algebras willbe held at Pomona College in Claremont, California, from July 25through August 7, 1999. This series of conferences emphasizes bothBanach algebras and their connections with other areas of analysis.The title of this conference is "Banach Algebras and Operators onBanach Spaces". The formal conference program will involve aboutsixty talks on the general theory of Banach algebras, on concreteBanach algebras, and on related areas of analysis. Some areasthat will be emphasized in the talks include automatic continuity,amenability and Banach homology, structure of Banach algebras,spectral theories and operator theory, group algebras and otherconvolution algebras, and complex analytic methods.One of the great accomplishments of modern mathematics is abstraction.Much like the way elementary algebra generalizes arithmetic, abstractiongives mathematicians the power to solve not only individual problems,but entire classes of problems. One of the most important twentieth-century examples is the field called functional analysis. Functionalanalysis uses new abstract techniques to treat problems that had beenstudied for more than two hundred years by what we now call classicalanalysis, which is the collection of methods that grew out of the calculus.Functional analysis, instead of concentrating on individual functions,studies spaces of functions and abstractions of such spaces. Not onlycould new problems and previously intractable old problems be solved bycombining the new and old methods, but the new structures of functionalanalysis also provided a new language which was needed to express many ofthe results of modern physics and, later, of other areas of science andof economics. The spaces considered by functional analysis all have somesort of operation of addition, but many of the most important spaces haveother operations as well. In particular, Banach algebras and relatedareas involve the very large and important collection of problems andstructures which have some sort of multiplication as well as the usualaddition. By the 1960s, Banach algebras, the subject of the conference, had become a recognized field of mathematics. Since 1974 the regularinternational conferences on Banach algebras have become an importantway for researchers worldwide to keep abreast of the field, to initiateand continue research collaborations, and to exchange ideas with researchersin related areas.