Given a C^＊-algebra A and a comultiplication Ф on A, we show that the pair （A, Ф） is a compact quantum group if and only if the associated multiplier Hopf ^＊-algebra （A, ФA） is a compact Hopf ^＊-algebra.
基金Acknowledgements The authors would like to thank the referees for their many invaluable suggestions. This work was supported by the Higher School Science and Technology Development Fund Project in Tianjin （Grant No. 20031003） and the National Natural Science Foundation of China （Grant No. 11301380）.
文摘Given a C^＊-algebra A and a comultiplication Ф on A, we show that the pair （A, Ф） is a compact quantum group if and only if the associated multiplier Hopf ^＊-algebra （A, ФA） is a compact Hopf ^＊-algebra.
