Banach algebras associated to locally compact groups

设G是群，即G是一个具有结合运算的集合，使得每个元素都有一个逆。例如，G可以被认为是正数或负数加上加法的集合，或者是正交变换的集合，即，线性变换后跟平移(仿射群)。在接下来的几年里，我的研究将包括：(A)研究与G相关的Banach代数(例如群代数、测度代数和傅立叶Stieltjes代数B(G))上的几何、代数和拓扑性质(B)研究由G(C)的左正则表示生成的von Neumann代数VN(G)中对应的非交换函数空间的对偶Banach代数的对偶Banach代数。

Let G be a group, i.e. G is a set with an associative operation such that each element has an inverse. For example, G may be taken to be the set of numbers, positive or negative, with addition, or the set of orthogonal transformations i.e. a linear transformation followed by translation (the affine group). My research in the next few years will consist of (a) the study of geometric, algebraic and topological properties on Banach algebras associated for G (e.g. group algebra, measure algebra and the Fourier Stieltjes algebra B(G) (b) the study of dual Banach algebras of the corresponding non-commutative function space in the von Neumann algebra VN(G) generated by the left regular representation of G (c) the (non-associative) Jordan structure in VN(G) for the fixed point set of a function in B(G).