Approximate similarity of operators on l^p

Analysis Seminar
Wednesday, April 25, 2018 - 1:55am
1 hour (actually 50 minutes)
Skiles 005
Abstract: I will state a version of Voiculescu's noncommutative Weyl-von Neumann theorem for operators on l^p that I obtained. This allows certain classical results concerning unitary equivalence of operators on l^2 to be generalized to operators on l^p if we relax unitary equivalence to similarity. For example, the unilateral shift on l^p, 1<p<\infty, is similar to a compact perturbation of the direct sum of the unilateral shift and the bilateral shift. When p=2, this is a classical result and similarity can be chosen to be unitary equivalence.