On concentration of convolutions of double cosets at infinite-dimensional limit

For infinite-dimensional groups $G\supset K$ the double cosets $K\setminus G/K$quiteoftenadmitastructureofasemigroup;thesesemigroupsactin$K$-fixedvectorsofunitaryrepresentationsof$G$. We show that such semigroups can be obtained as limits of double cosets hypergroups (or Iwahori–Hecke type algebras) on finite-dimensional (or finite) groups.