Hille's theorem for Bochner integrals of functions with values in locally convex spaces

Abstract

Hille's theorem is a powerful classical result in vector measure theory. It asserts that the application of a closed, unbounded linear operator commutes with strong/Bochner integration of functions taking values in a Banach space. This note shows that Hille's theorem also holds in the setting of complete locally convex spaces.

arXiv comment9 pages