Banach algebras associated to locally compact groups

设G是一个群，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可以被认为是一组数字，正的或负的，加上，或一组正交变换，即一个线性变换后的平移（仿射群）。 我在今后几年的研究工作将包括：（a）研究G的Banach代数的几何、代数和拓扑性质（例如群代数，测度代数与Fourier Stieltjes代数B（G）（B）研究了对偶Banach代数对应的非交换函数空间在von Neumann代数VN（G）上生成的G（c）的左正则表示B（G）中函数的不动点集在VN（G）中的（非结合）Jordan结构。

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).