Commutative Radical Banach Algebras

数学研究的一个相当具体的背景 在这个项目中进行的是电力系列， 可以被认为是无限次的多项式。放置 对生长（或衰退）的适当限制 这样一个系列的系数产生了一个Banach代数 Power系列可能唯一的评估方法 代数中的所有级数都是通过取常数 term.在这种情况下，有一个（交换）根Banach 代数，一个非常奇特的对象。最近，校长 研究人员证明了一个重要的结果， 推导（初等微积分中推导的类似物） 这样的Banach代数，从而解决 这个问题已经存在了三十多年。的 他开发的技术将被扩展并用于探索 其他结构性问题。

One fairly concrete setting for the mathematical research to be undertaken in this project is that of power series, which may be thought of as polynomials of infinite degree. Placing an appropriate constraint on the growth (or decay) of the coefficients of such a series gives rise to a Banach algebra of power series. It may happen that the only way to evaluate all of the series in the algebra is by taking the constant term. In this case, one has a (commutative) radical Banach algebra, a very exotic object. Recently, the principal investigator has proved an important result concerning derivations (analogues of the derivative in elementary calculus) of Banach algebras like these, thereby solving a problem that had been open for over thirty years. The techniques he developed will be extended and used to explore other structural questions.