Peetre's theorem in the locally convex setting

What is it about?

Peetre's Theorem gives a characterisation of differentiable operaters without explicitely mentioning derivates and therefore is of fundamental importance for differential calculus on manifolds. In this publication we generalize this theorem in the infinite dimensional setting.

Featured Image

Why is it important?

In infinite dimensions, many of the tools and results from finite dimensions break down. Thereofre, it is important to state which finite dimensional results can be carried over to infinite dimenions. This paper explains how Peetre's Theorem can be carried over to the case where the range space is infinite dimensional, as long as the domain stays finite dimensional.