Spaces of normal linear functionals
by
Marius Junge
Univarsity of Illinois
Coauthors: Javier Parcet

The predual of a von Neumann algebra contains viable information about the von Neumann algebra itself. Following a result of Pisier the von Neumann algebra N can not be semifinite if the produal contains the operator Hilbert space OH (with his inherited matrix structure). Note that of course every predual contains many space which are Hilbert spaces on the Banach space level. Thus the operator space structure is needed. In our talk we will construct more exotic subspaces of linear functionals in the predual of the hyperfinite III₁ factor. Indeed, we will show that for suitable nice Hilbertian operator space E and F the Haagerup tensor product E\ten_h F embeds in there. A recent result of Haagerup and Musat then shows that this is also true for some III₀ factors. -This is joint work with Javier Parcet

Date received: May 16, 2008