### #functional-analysis

### Hille's theorem for locally convex spaces in Real Analysis Exchange

The article “Hille's theorem for Bochner integrals of functions with values in locally convex spaces” has just appeared in its final form in *Real Analysis Exchange*.

T. J. Sullivan. “Hille's theorem for Bochner integrals of functions with values in locally convex spaces.” *Real Analysis Exchange* 49(2):377–388, 2024.

**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.

Published on Tuesday 1 October 2024 at 13:00 UTC #publication #real-anal-exch #functional-analysis #hille-theorem

### Hille’s theorem for locally convex spaces

I have just uploaded a preprint of the paper “Hille's theorem for Bochner integrals of functions with values in locally convex spaces” to the arXiv. This paper extends the relatively well known result that Bochner integration commutes with closed operators from the classical Banach space setting to the case of more general locally convex spaces.

Published on Thursday 18 January 2024 at 09:00 UTC #preprint #functional-analysis #hille-theorem