约化Banach代数的谱不变性和双曲群

Spectral Invariance of the Reduced Banach Algebras and Hyperbolic Groups

主要研究了可数离散群的性质SRD,并证明了具有性质SRD的群上的速降函数全体组成的空间是约化Banach代数谱不变的稠密子代数.最后作为例子给出了双曲群具有性质SRD.

In this paper, the authors mainly study property SRD for a countable discrete group. It is shown that the set of rapid-decay functions on strongly rapidly decaying group forms a dense and spectral invariant sub-algebra of the reduced Banach algebra. Finally, it is shown that hyperbolic groups have property SRD.