HAAR MEASURES ON HOPF C-ASTERISK-ALGEBRAS

In this paper, we first use Markov-Kakutani's fixed point theorem to prove the existence and uniqueness of Haar measures on cocommutative Hopf C*-algebras. Also we show that in the commutative case, there exists a natural one-to-one correspondence between the Haar measure on a given Hopf C*-algebra and Haar measures on the associated semigroup. Finally, we show that for Hopf C*-algebras with Peter-Weyl property, they have Haar measures.