Approximate amenability for Banach algebras

Banach代数是一种同时具有代数结构和拓扑结构的抽象数学对象，数学家们迫切希望研究这两种结构之间的关系。他们这样做是因为抽象对象本身似乎是美丽和有趣的，但更多的是因为这些对象涵盖了数学中许多自然发生的例子。一个非常成功的研究方向涵盖了服从Banach代数的研究，并且在这种代数上有许多精细的定理。然而，这一概念并不涵盖所有适当的情况，现在有相当多的研究这一基本思想的变化。其中一些变体是由Ghahramani和Loy引入的；本质上，他们现在考虑的是近似服从的Banach代数。我建议与澳大利亚国立大学的R.J.Loy博士合作研究这些变体，并确定哪些特定的Banach代数具有相关的性质，以期形成一个一般的理论。

A Banach algebra is an abstract mathematical object that has both an algebraic and a topological structure, and mathematicians are eager to study the relationship of these two structures. They do this because the abstract objects seem to be of beauty and interest in their own right, but more because these objects cover many naturally occurring examples in mathematics.A very successful line of investigation covers that of amenable Banach algebras, and there are many fine theorems on such algebras. Nevertheless this concept does not cover all appropriate circumstances, and there is now considerable study of variations of this fundamental idea. Some of these variations were introduced by Ghahramani and Loy; essentially, they now consider approximately amenable Banach algebras .I propose to work with Dr. R. J. Loy (Australian National University, Canberra) to study these variants and determine which specfic Banach algebras possess the relevant properties, with a view to formulating a general theory.