Linear Analysis Seminar

Date: October 28, 2016

Time: 4:00PM - 5:00PM

Location: BLOC 220

Speaker: Jason Crann, Carleton University

Title: Module injectivity of group von Neumann algebras

Abstract: This talk will feature recent results on the injectivity of VN(G) as an operator module over the Fourier algebra A(G) for general locally compact (quantum) groups G. Contrary to the operator space category, we show that amenability of G is equivalent to injectivity of VN(G), and present a variety of applications. In the group setting, we show that inner amenability of G is equivalent to relative injectivity of VN(G). This result, among other things, allows us to answer 3 open questions in abstract harmonic analysis. In the bimodule setting, we characterize the (relative) injectivity of VN(G) and apply our results to elucidate the operator amenability of Acb(G) - the cb-multiplier norm closure of A(G).