Author(s)

Jicheng Tao¹, Wen Yan²

¹Department of Mathematics, China Jiliang University, Hangzhou, China.
²Department of Mathematics, Tuskegee University, Tuskegee, USA.

In this paper, we investigate Kazhdan’s relative Property (T) for pairs , where is a topological group and is any subset of . We show that the pair has Property (FH) and every function conditionally of negative type on is X-bounded if the pair has relative Property (T). We also prove that has Property (T) whenis a s -compact locally compact group generated by its subgroups and the pair has relative Property (T) for all .

Relative Property (T) of Topological Group, Function Conditionally of Negative Type, Property (FH)

Tao, J. and Yan, W. (2014) Relative Property (T) for Topological Groups. Applied Mathematics, 5, 2988-2993. doi: 10.4236/am.2014.519285.