Operator Theory Seminar
One of the most important outstanding problems in von Neumann algebras asks if the group von Neumann algebra of the free group on two generators, denoted by L(F2), is isomorphic to the group von Neumann algebra of the free group on infinitely many generators, denoted by L(F∞). Recently, S. Popa established a roadmap for showing the nonisomorphism of L(F2) and L(F∞). The first step of the proposed roadmap is to establish the so-called mean value property (abbreviated MV-property) for L(F2).
In this talk I shall describe the proof of the result that L(F2) has the MV-property, thereby establishing the first step of Popa's roadmap. This talk is based on a recent joint work with Prof. Jesse Peterson.