Aspects of locally compact quantum groups

2017-01-24T00:50:06Z (GMT) by Heidarirad, Zohreh
The aim of this thesis is to genaralize some concepts of abstract harmonic analysis to locally compact quantum groups. In fact, for a locally compact quantum group G, we replace functions on locally compact groups by elements of von Neumann algebras with additional structure. The fist part of the thesis is devoted to the study of some properties of the Fourier transform on locally compact quantum groups. In the second part of the thesis we introduce uniform continuity and (weak) almost periodicity on locally compact quantum groups. Furthermore, we provide another characterization of amenability of locally compact quantum groups.