Positive definite $\ast$-spherical functions, property (T), and $C^{\ast }$-completions of Gelfand pairs

Nadia S. Larsen, Rui Palma

The study of existence of a universal $C^{\ast }$-completion of the ${}^{\ast }$-algebra canonically associated to a Hecke pair was initiated by Hall, who proved that the Hecke algebra associate…