Multipliers of locally compact quantum groups via Hilbert C*-modules

作者：Daws Matthew^*

来源：Journal of the London Mathematical Society-Second Series, 2011, 84: 385-407.

DOI：10.1112/jlms/jdr013

A result of Gilbert shows that every completely bounded multiplier f of the Fourier algebra A(G) arises from a pair of bounded continuous maps alpha, beta : G -> K, where K is a Hilbert space, and f(s(-1)t) = (beta(t) vertical bar alpha (s)) for all s, t epsilon G. We recast this in terms of adjointable operators acting between certain Hilbert C*-modules, and show that an analogous construction works for completely bounded left multipliers of a locally compact quantum group. We find various ways to deal with right multipliers: one of these involves looking at the opposite quantum group, and this leads to a proof that the (unbounded) antipode acts on the space of completely bounded multipliers in a way that interacts naturally with our representation result. The dual of the universal quantum group (in the sense of Kustermans) can be identified with a subalgebra of the completely bounded multipliers, and we show how this fits into our framework. Finally, this motivates a certain way of dealing with two-sided multipliers.

• 出版日期2011-10