A characterization of compact quantum groups through second duals

نویسنده

  • Volker Runde
چکیده

A locally compact group G is compact if and only if L(G) is an ideal in L(G). On the other hand, the Fourier algebra A(G) of G is an ideal in A(G)∗∗ if and only if G is discrete. We show that both results are special cases of one general theorem on locally compact quantum groups in the sense of J. Kustermans and S. Vaes: a von Neumann algebraic quantum group (M,Γ) is compact if and only if M∗ is an ideal in M∗.

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تاریخ انتشار 2005