Speaker: Stuart White
Affiliation: Texas A&M University
Title: Generators of II_1 factors.
Time and Place: Thursday, April 26, 3:00-3:50pm, Milner 317.
Abstract:
The generator problem asks whether every von Neumann algebra acting on
a separable Hilbert space is generated by 2 self-adjoint elements. In
the 1960's work of Douglas, Pearcy, Topping, Wogen and others reduced
this problem to the case of II_1 factors. Many II_1 factors with nice
decomposition properties (such as having a Cartan masa) are also known
to be singly generated via work of Ge, Popa, and others. Recently Shen
has defined an invariant G(M) of a II_1 factor M and shown that if
G(M)<1/4, then M is singly generated. This gives a unified
approach to all the known examples of singly generated II_1 factors,
and the basic ideas involve the matrix calculations of Douglas,
Pearcy, et al.
In this talk I shall discuss this recent development and examine
certain properties of the invariant G(M) such as the behaviour under
amplifications. I intend to spend some time covering the earlier work
from the 60's, in particular Wogen's theorem that every properly
infinite von Neumann algebra on a separable Hilbert space is singly
generated.