Mathematical Sciences: The Structure of Non-Semisimple Banach Algebras

柯蒂斯教授和巴德教授将继续研究非半简单巴拿赫代数中的基与包含它的代数之间的潜在结构关系。这个问题将在可调或弱可调巴拿赫代数的背景下讨论。将特别注意由非谱合成集产生的非半简单代数、局部紧阿贝尔群的群代数和相关的伯林代数。巴拿赫代数是由可以相加或相乘的抽象对象组成的，但故意不指定乘法规则的确切形式，以便得到的结果适用于很多情况。巴拿赫代数的具体例子很多，本研究将有助于阐明其结构。

Professors Curtis and Bade will continue their research into the underlying structural relationship between the radical in a non-semisimple Banach algebra and the algebra which contains it. This problem will be pursued in the context of amenable or weakly amenable Banach algebras. Particular attention will be paid to non-semisimple algebras arising from sets of non spectral synthesis for group algebras of locally compact abelian groups and for the associated Beurling algebras. Banach algebras are composed of abstract objects which can be added or multiplied, but the exact form of the multiplication rule is purposely not specified so that the results obtained apply to very many situations. Concrete examples of Banach algebras are plentiful, and this research will help elucidate their structure.