Texas A&M University, Department of
Mathematics, 216 Milner Hall, 3rd of October 2007, 3:00-3:50
Groups and Dynamics Seminar
Weak mixing and l_1
David Kerr of Texas A&M University
Rosenthal's l_1 theorem gives a local characterization of Banach spaces
containing l_1 in terms of a dichotomy between randomness and
compactness. For unitary representations of groups there is an analogous
dichotomy involving weak mixing and finite-dimensional
subrepresentations. I will show that, despite the topological nature of
Rosenthal's l_1 theorem, in the context of measurable dynamics these two
dichotomies provide different means for describing the same phenomenon.
This is joint work with Hanfeng Li.