Nonlinear Analysis and Optimization Seminar[ Edit ]
Moderator: Simeon Reich
A Banach limit is a classical way in functional analysis to assign "limits" to bounded non-convergent sequences. The method can be extended to assign limits to bounded sequences of convex bodies. The geometric mean of two convex bodies is a new construct studied by myself and V. Milman following a construction of Firey. In this talk we will see the interplay between the two notions. On the one hand, we will see how the geometric mean can be used to create a Banach limit that commutes with duality. On the other hand, we will see how Banach limits can be used to create a new version of the geometric mean with more desirable properties. No previous knowledge of Banach limits or of convex geometry will be assumed.