Zhiguo Hu, University of Windsor
“Strong irregularity of the trace class convolution algebra”
For a locally compact quantum group G, the space T(L2(G)) of trace class operators on L2(G) is a completely contractive Banach algebra with the multiplication induced by the right fundamental unitary of G. We will discuss the strong Arens irregularity (in the sense of Dales- Lau) of this convolution algebra. We show that T(L2(G)) is strongly Arens irregular if and only if the quantum group G is finite. This yields a natural class of Banach algebras associated with quantum groups for which Arens regularity and strong Arens irregularity are, surprisingly, equivalent. This talk is based on joint work with Matthias Neufang and Zhong-Jin Ruan.