 The universal construction is also used to define universal C*-algebras of isometries.Remark.The Gelfand representation or Gelfand isomorphism for a commutative C*-algebra with unit formula_6 is an isometric *-isomorphism from formula_6 to the algebra of continuous complex-valued functions on the space of multiplicative linear functionals, which in the commutative case are precisely the pure states, of "A" with the weak* topology.