an:07040651
Zbl 1417.46047
Medghalchi, Alireza; Mollakhalili, Ahmad
Compact and weakly compact multipliers of locally compact quantum groups
EN
Bull. Iran. Math. Soc. 44, No. 1, 101-136 (2018).
00430156
2018
j
46L89 22D25 46L51
locally compact quantum groups; (weakly) compact operators; amenability; module homomorphims
Summary: A locally compact group \(G\) is compact if and only if its convolution algebra has a non-zero (weakly) compact multiplier. Dually, \(G\) is discrete if and only if its Fourier algebra has a non-zero (weakly) compact multiplier. In addition, \(G\) is compact (respectively, amenable) if and only if the second dual of its convolution algebra equipped with the first Arens product has a non-zero (weakly) compact left (respectively, right) multiplier. We prove the non-commutative versions of these results in the case of locally compact quantum groups.