2011-09-27 Seminar

Professor David Yost
(University of Ballarat, Australia)

Norm one projections in Banach spaces

On all of the familiar Banach spaces, it is very easy to write down a formula which defines a norm one (linear) projection. This is not true for arbitrary Banach spaces. The following rough trichotomy indicates the range of behaviour.

1. Most finite dimensional Banach spaces admit no norm one projections at all (except those with rank one). Such examples may be smooth, strictly convex, or polyhedral.
2. Some separable Banach spaces admit no continuous projections at all (except those with finite rank or co-rank).
3. Many non-separable Banach spaces admit many nontrivial norm one projections, even under every equivalent norm.

The seminar is going to take place at 10:00 in B3-38.